Daily Papers

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

We investigate feature universality in large language models (LLMs), a research field that aims to understand how different models similarly represent concepts in the latent spaces of their intermediate layers. Demonstrating feature universality allows discoveries about latent representations to generalize across several models. However, comparing features across LLMs is challenging due to polysemanticity, in which individual neurons often correspond to multiple features rather than distinct ones. This makes it difficult to disentangle and match features across different models. To address this issue, we employ a method known as dictionary learning by using sparse autoencoders (SAEs) to transform LLM activations into more interpretable spaces spanned by neurons corresponding to individual features. After matching feature neurons across models via activation correlation, we apply representational space similarity metrics like Singular Value Canonical Correlation Analysis to analyze these SAE features across different LLMs. Our experiments reveal significant similarities in SAE feature spaces across various LLMs, providing new evidence for feature universality.

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

Selecting a suitable training dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this data selection problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution, given some unlabeled target samples. Due to the large scale and dimensionality of the raw text data, existing methods use simple heuristics to select data that are similar to a high-quality reference corpus (e.g., Wikipedia), or leverage experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. Crucially, we work in a reduced feature space to make importance weight estimation tractable over the space of text. To determine an appropriate feature space, we first show that KL reduction, a data metric that measures the proximity between selected data and the target in a feature space, has high correlation with average accuracy on 8 downstream tasks (r=0.89) when computed with simple n-gram features. From this observation, we present Data Selection with Importance Resampling (DSIR), an efficient and scalable algorithm that estimates importance weights in a reduced feature space (e.g., n-gram features in our instantiation) and selects data with importance resampling according to these weights. When training general-domain models (target is Wikipedia + books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark. When performing continued pretraining towards a specific domain, DSIR performs comparably to expert curated data across 8 target distributions.

We present our vision for developing an automated tool capable of translating visual properties observed in Machine Learning (ML) visualisations into Python assertions. The tool aims to streamline the process of manually verifying these visualisations in the ML development cycle, which is critical as real-world data and assumptions often change post-deployment. In a prior study, we mined 54,070 Jupyter notebooks from Github and created a catalogue of 269 semantically related visualisation-assertion (VA) pairs. Building on this catalogue, we propose to build a taxonomy that organises the VA pairs based on ML verification tasks. The input feature space comprises of a rich source of information mined from the Jupyter notebooks -- visualisations, Python source code, and associated markdown text. The effectiveness of various AI models, including traditional NLP4Code models and modern Large Language Models, will be compared using established machine translation metrics and evaluated through a qualitative study with human participants. The paper also plans to address the challenge of extending the existing VA pair dataset with additional pairs from Kaggle and to compare the tool's effectiveness with commercial generative AI models like ChatGPT. This research not only contributes to the field of ML system validation but also explores novel ways to leverage AI for automating and enhancing software engineering practices in ML.

Click-through prediction (CTR) models transform features into latent vectors and enumerate possible feature interactions to improve performance based on the input feature set. Therefore, when selecting an optimal feature set, we should consider the influence of both feature and its interaction. However, most previous works focus on either feature field selection or only select feature interaction based on the fixed feature set to produce the feature set. The former restricts search space to the feature field, which is too coarse to determine subtle features. They also do not filter useless feature interactions, leading to higher computation costs and degraded model performance. The latter identifies useful feature interaction from all available features, resulting in many redundant features in the feature set. In this paper, we propose a novel method named OptFS to address these problems. To unify the selection of feature and its interaction, we decompose the selection of each feature interaction into the selection of two correlated features. Such a decomposition makes the model end-to-end trainable given various feature interaction operations. By adopting feature-level search space, we set a learnable gate to determine whether each feature should be within the feature set. Because of the large-scale search space, we develop a learning-by-continuation training scheme to learn such gates. Hence, OptFS generates the feature set only containing features which improve the final prediction results. Experimentally, we evaluate OptFS on three public datasets, demonstrating OptFS can optimize feature sets which enhance the model performance and further reduce both the storage and computational cost.

Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes. However, we believe that the potential offered by this paradigm is not yet fully exploited. In this work, we propose to utilize the structure of the space spanned by the attributes using a set of relations. We devise objective functions to preserve these relations in the embedding space, thereby inducing semanticity to the embedding space. Through extensive experimental evaluation on five benchmark datasets, we demonstrate that inducing semanticity to the embedding space is beneficial for zero-shot learning. The proposed approach outperforms the state-of-the-art on the standard zero-shot setting as well as the more realistic generalized zero-shot setting. We also demonstrate how the proposed approach can be useful for making approximate semantic inferences about an image belonging to a category for which attribute information is not available.

Self-supervised features are the cornerstone of modern machine learning systems. They are typically pre-trained on data collections whose construction and curation typically require extensive human effort. This manual process has some limitations similar to those encountered in supervised learning, e.g., the crowd-sourced selection of data is costly and time-consuming, preventing scaling the dataset size. In this work, we consider the problem of automatic curation of high-quality datasets for self-supervised pre-training. We posit that such datasets should be large, diverse and balanced, and propose a clustering-based approach for building ones satisfying all these criteria. Our method involves successive and hierarchical applications of k-means on a large and diverse data repository to obtain clusters that distribute uniformly among data concepts, followed by a hierarchical, balanced sampling step from these clusters. Extensive experiments on three different data domains including web-based images, satellite images and text show that features trained on our automatically curated datasets outperform those trained on uncurated data while being on par or better than ones trained on manually curated data.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

We investigate the construction of latent spaces through self-supervised learning to support semantically meaningful operations. Analogous to operational amplifiers, these "operational latent spaces" (OpLaS) not only demonstrate semantic structure such as clustering but also support common transformational operations with inherent semantic meaning. Some operational latent spaces are found to have arisen "unintentionally" in the progress toward some (other) self-supervised learning objective, in which unintended but still useful properties are discovered among the relationships of points in the space. Other spaces may be constructed "intentionally" by developers stipulating certain kinds of clustering or transformations intended to produce the desired structure. We focus on the intentional creation of operational latent spaces via self-supervised learning, including the introduction of rotation operators via a novel "FiLMR" layer, which can be used to enable ring-like symmetries found in some musical constructions.

Recent advances in large vision-language models have revolutionized the image classification paradigm. Despite showing impressive zero-shot capabilities, a pre-defined set of categories, a.k.a. the vocabulary, is assumed at test time for composing the textual prompts. However, such assumption can be impractical when the semantic context is unknown and evolving. We thus formalize a novel task, termed as Vocabulary-free Image Classification (VIC), where we aim to assign to an input image a class that resides in an unconstrained language-induced semantic space, without the prerequisite of a known vocabulary. VIC is a challenging task as the semantic space is extremely large, containing millions of concepts, with hard-to-discriminate fine-grained categories. In this work, we first empirically verify that representing this semantic space by means of an external vision-language database is the most effective way to obtain semantically relevant content for classifying the image. We then propose Category Search from External Databases (CaSED), a method that exploits a pre-trained vision-language model and an external vision-language database to address VIC in a training-free manner. CaSED first extracts a set of candidate categories from captions retrieved from the database based on their semantic similarity to the image, and then assigns to the image the best matching candidate category according to the same vision-language model. Experiments on benchmark datasets validate that CaSED outperforms other complex vision-language frameworks, while being efficient with much fewer parameters, paving the way for future research in this direction.

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising weight-space models that are equivariant to the permutation symmetries of simple feedforward networks. However, they are not applicable to general architectures, since the permutation symmetries of a weight space can be complicated by recurrence or residual connections. This work proposes an algorithm that automatically constructs permutation equivariant models, which we refer to as universal neural functionals (UNFs), for any weight space. Among other applications, we demonstrate how UNFs can be substituted into existing learned optimizer designs, and find promising improvements over prior methods when optimizing small image classifiers and language models. Our results suggest that learned optimizers can benefit from considering the (symmetry) structure of the weight space they optimize. We open-source our library for constructing UNFs at https://github.com/AllanYangZhou/universal_neural_functional.

The design of modern recommender systems relies on understanding which parts of the feature space are relevant for solving a given recommendation task. However, real-world data sets in this domain are often characterized by their large size, sparsity, and noise, making it challenging to identify meaningful signals. Feature ranking represents an efficient branch of algorithms that can help address these challenges by identifying the most informative features and facilitating the automated search for more compact and better-performing models (AutoML). We introduce OutRank, a system for versatile feature ranking and data quality-related anomaly detection. OutRank was built with categorical data in mind, utilizing a variant of mutual information that is normalized with regard to the noise produced by features of the same cardinality. We further extend the similarity measure by incorporating information on feature similarity and combined relevance. The proposed approach's feasibility is demonstrated by speeding up the state-of-the-art AutoML system on a synthetic data set with no performance loss. Furthermore, we considered a real-life click-through-rate prediction data set where it outperformed strong baselines such as random forest-based approaches. The proposed approach enables exploration of up to 300% larger feature spaces compared to AutoML-only approaches, enabling faster search for better models on off-the-shelf hardware.

Existing works on visual counting primarily focus on one specific category at a time, such as people, animals, and cells. In this paper, we are interested in counting everything, that is to count objects from any category given only a few annotated instances from that category. To this end, we pose counting as a few-shot regression task. To tackle this task, we present a novel method that takes a query image together with a few exemplar objects from the query image and predicts a density map for the presence of all objects of interest in the query image. We also present a novel adaptation strategy to adapt our network to any novel visual category at test time, using only a few exemplar objects from the novel category. We also introduce a dataset of 147 object categories containing over 6000 images that are suitable for the few-shot counting task. The images are annotated with two types of annotation, dots and bounding boxes, and they can be used for developing few-shot counting models. Experiments on this dataset shows that our method outperforms several state-of-the-art object detectors and few-shot counting approaches. Our code and dataset can be found at https://github.com/cvlab-stonybrook/LearningToCountEverything.

A common approach for sequence tagging tasks based on contextual word representations is to train a machine learning classifier directly on these embedding vectors. This approach has two shortcomings. First, such methods consider single input sequences in isolation and are unable to put an individual embedding vector in relation to vectors outside the current local context of use. Second, the high performance of these models relies on fine-tuning the embedding model in conjunction with the classifier, which may not always be feasible due to the size or inaccessibility of the underlying feature-generation model. It is thus desirable, given a collection of embedding vectors of a corpus, i.e., a datastore, to find features of each vector that describe its relation to other, similar vectors in the datastore. With this in mind, we introduce complexity measures of the local topology of the latent space of a contextual language model with respect to a given datastore. The effectiveness of our features is demonstrated through their application to dialogue term extraction. Our work continues a line of research that explores the manifold hypothesis for word embeddings, demonstrating that local structure in the space carved out by word embeddings can be exploited to infer semantic properties.

Large language models have transformed natural language processing, yet supervised fine-tuning (SFT) remains computationally intensive. This paper formally proves that capabilities acquired through SFT can be approximated by a base transformer model using inference-time techniques, specifically in-context learning (ICL), without altering model parameters, under idealized assumptions including unbounded computational resources and access to the fine-tuning dataset. We extend these results to practical scenarios with finite context lengths and partial dataset access. For text generation tasks with fixed output length l, datasets of size Oleft( m V{varepsilon^2} log m{delta} right) or, with bounded context, Oleft( l log V{varepsilon^2} log 1{delta} right) suffice to approximate fine-tuned behavior across m contexts within error varepsilon, where V is the vocabulary size and delta is the failure probability. For linear classification, datasets of size Oleft( d{varepsilon} right) or, with fixed context, Oleft( 1{varepsilon^2} log 1{delta} right) are sufficient, where d is the input dimension. Grounded in the Turing completeness of transformers, these results provide a theoretical foundation for resource-efficient deployment of large language models, with practical techniques like retrieval-augmented generation bridging theory to real-world applications.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

In this paper, we propose a method to partially mimic natural intelligence for the problem of lifelong learning representations that are compatible. We take the perspective of a learning agent that is interested in recognizing object instances in an open dynamic universe in a way in which any update to its internal feature representation does not render the features in the gallery unusable for visual search. We refer to this learning problem as Compatible Lifelong Learning Representations (CL2R) as it considers compatible representation learning within the lifelong learning paradigm. We identify stationarity as the property that the feature representation is required to hold to achieve compatibility and propose a novel training procedure that encourages local and global stationarity on the learned representation. Due to stationarity, the statistical properties of the learned features do not change over time, making them interoperable with previously learned features. Extensive experiments on standard benchmark datasets show that our CL2R training procedure outperforms alternative baselines and state-of-the-art methods. We also provide novel metrics to specifically evaluate compatible representation learning under catastrophic forgetting in various sequential learning tasks. Code at https://github.com/NiccoBiondi/CompatibleLifelongRepresentation.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational limits, particularly spatial complexity constrained by finite context windows, remain poorly understood. While recent works often focus on problems within the NP complexity class, we push the boundary by introducing a novel benchmark grounded in two PSPACE-complete regular expression (regex) problems: equivalence decision (RegexEQ) and minimization (RegexMin). PSPACE-complete problems serve as a more rigorous standard for assessing computational capacity, as their solutions require massive search space exploration. We perform a double-exponential space exploration to construct a labeled dataset of over a million regex instances with a sound filtering process to build the benchmark. We conduct extensive evaluations on 6 LLMs and 5 LRMs of varying scales, revealing common failure patterns such as verbosity and repetition. With its well-defined structure and quantitative evaluation metrics, this work presents the first empirical investigation into the spatial computational limitations of LLMs and LRMs, offering a new framework for evaluating their advanced reasoning capabilities. Our code is available at https://github.com/hyundong98/RegexPSPACE .

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

In this paper, we consider the problem of generalised visual object counting, with the goal of developing a computational model for counting the number of objects from arbitrary semantic categories, using arbitrary number of "exemplars", i.e. zero-shot or few-shot counting. To this end, we make the following four contributions: (1) We introduce a novel transformer-based architecture for generalised visual object counting, termed as Counting Transformer (CounTR), which explicitly capture the similarity between image patches or with given "exemplars" with the attention mechanism;(2) We adopt a two-stage training regime, that first pre-trains the model with self-supervised learning, and followed by supervised fine-tuning;(3) We propose a simple, scalable pipeline for synthesizing training images with a large number of instances or that from different semantic categories, explicitly forcing the model to make use of the given "exemplars";(4) We conduct thorough ablation studies on the large-scale counting benchmark, e.g. FSC-147, and demonstrate state-of-the-art performance on both zero and few-shot settings.

The objective of pre-trained language models is to learn contextual representations of textual data. Pre-trained language models have become mainstream in natural language processing and code modeling. Using probes, a technique to study the linguistic properties of hidden vector spaces, previous works have shown that these pre-trained language models encode simple linguistic properties in their hidden representations. However, none of the previous work assessed whether these models encode the whole grammatical structure of a programming language. In this paper, we prove the existence of a syntactic subspace, lying in the hidden representations of pre-trained language models, which contain the syntactic information of the programming language. We show that this subspace can be extracted from the models' representations and define a novel probing method, the AST-Probe, that enables recovering the whole abstract syntax tree (AST) of an input code snippet. In our experimentations, we show that this syntactic subspace exists in five state-of-the-art pre-trained language models. In addition, we highlight that the middle layers of the models are the ones that encode most of the AST information. Finally, we estimate the optimal size of this syntactic subspace and show that its dimension is substantially lower than those of the models' representation spaces. This suggests that pre-trained language models use a small part of their representation spaces to encode syntactic information of the programming languages.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We present a dataset of large-scale indoor spaces that provides a variety of mutually registered modalities from 2D, 2.5D and 3D domains, with instance-level semantic and geometric annotations. The dataset covers over 6,000m2 and contains over 70,000 RGB images, along with the corresponding depths, surface normals, semantic annotations, global XYZ images (all in forms of both regular and 360{\deg} equirectangular images) as well as camera information. It also includes registered raw and semantically annotated 3D meshes and point clouds. The dataset enables development of joint and cross-modal learning models and potentially unsupervised approaches utilizing the regularities present in large-scale indoor spaces. The dataset is available here: http://3Dsemantics.stanford.edu/

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

Ad-hoc Video Search (AVS) involves using a textual query to search for multiple relevant videos in a large collection of unlabeled short videos. The main challenge of AVS is the visual diversity of relevant videos. A simple query such as "Find shots of a man and a woman dancing together indoors" can span a multitude of environments, from brightly lit halls and shadowy bars to dance scenes in black-and-white animations. It is therefore essential to retrieve relevant videos as comprehensively as possible. Current solutions for the AVS task primarily fuse multiple features into one or more common spaces, yet overlook the need for diverse spaces. To fully exploit the expressive capability of individual features, we propose LPD, short for Learning Partially Decorrelated common spaces. LPD incorporates two key innovations: feature-specific common space construction and the de-correlation loss. Specifically, LPD learns a separate common space for each video and text feature, and employs de-correlation loss to diversify the ordering of negative samples across different spaces. To enhance the consistency of multi-space convergence, we designed an entropy-based fair multi-space triplet ranking loss. Extensive experiments on the TRECVID AVS benchmarks (2016-2023) justify the effectiveness of LPD. Moreover, diversity visualizations of LPD's spaces highlight its ability to enhance result diversity.

We address the problem of few-shot pattern detection, which aims to detect all instances of a given pattern, typically represented by a few exemplars, from an input image. Although similar problems have been studied in few-shot object counting and detection (FSCD), previous methods and their benchmarks have narrowed patterns of interest to object categories and often fail to localize non-object patterns. In this work, we propose a simple yet effective detector based on template matching and regression, dubbed TMR. While previous FSCD methods typically represent target exemplars as spatially collapsed prototypes and lose structural information, we revisit classic template matching and regression. It effectively preserves and leverages the spatial layout of exemplars through a minimalistic structure with a small number of learnable convolutional or projection layers on top of a frozen backbone We also introduce a new dataset, dubbed RPINE, which covers a wider range of patterns than existing object-centric datasets. Our method outperforms the state-of-the-art methods on the three benchmarks, RPINE, FSCD-147, and FSCD-LVIS, and demonstrates strong generalization in cross-dataset evaluation.

We present Franca (pronounced Fran-ka): free one; the first fully open-source (data, code, weights) vision foundation model that matches and in many cases surpasses the performance of state-of-the-art proprietary models, e.g., DINOv2, CLIP, SigLIPv2, etc. Our approach is grounded in a transparent training pipeline inspired by Web-SSL and uses publicly available data: ImageNet-21K and a subset of ReLAION-2B. Beyond model release, we tackle critical limitations in SSL clustering methods. While modern models rely on assigning image features to large codebooks via clustering algorithms like Sinkhorn-Knopp, they fail to account for the inherent ambiguity in clustering semantics. To address this, we introduce a parameter-efficient, multi-head clustering projector based on nested Matryoshka representations. This design progressively refines features into increasingly fine-grained clusters without increasing the model size, enabling both performance and memory efficiency. Additionally, we propose a novel positional disentanglement strategy that explicitly removes positional biases from dense representations, thereby improving the encoding of semantic content. This leads to consistent gains on several downstream benchmarks, demonstrating the utility of cleaner feature spaces. Our contributions establish a new standard for transparent, high-performance vision models and open a path toward more reproducible and generalizable foundation models for the broader AI community. The code and model checkpoints are available at https://github.com/valeoai/Franca.

We introduce a novel method for representation learning that uses an artificial supervision signal based on counting visual primitives. This supervision signal is obtained from an equivariance relation, which does not require any manual annotation. We relate transformations of images to transformations of the representations. More specifically, we look for the representation that satisfies such relation rather than the transformations that match a given representation. In this paper, we use two image transformations in the context of counting: scaling and tiling. The first transformation exploits the fact that the number of visual primitives should be invariant to scale. The second transformation allows us to equate the total number of visual primitives in each tile to that in the whole image. These two transformations are combined in one constraint and used to train a neural network with a contrastive loss. The proposed task produces representations that perform on par or exceed the state of the art in transfer learning benchmarks.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to 20times sim 5000times. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts. To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in various multimodal tasks. To pursue higher intelligence in space, MLLMs require integrating multiple atomic spatial capabilities to handle complex and dynamic tasks. However, existing benchmarks struggle to comprehensively evaluate the spatial intelligence of common MLLMs from the atomic level to the compositional level. To fill this gap, we present SpaCE-10, a comprehensive benchmark for compositional spatial evaluations. In SpaCE-10, we define 10 atomic spatial capabilities, which are combined to form 8 compositional capabilities. Based on these definitions, we propose a novel hierarchical annotation pipeline to generate high-quality and diverse question-answer (QA) pairs. With over 150+ hours of human expert effort, we obtain over 5k QA pairs for 811 real indoor scenes in SpaCE-10, which covers various evaluation settings like point cloud input and multi-choice QA. We conduct an extensive evaluation of common MLLMs on SpaCE-10 and find that even the most advanced MLLM still lags behind humans by large margins. Through our careful study, we also draw several significant findings that benefit the MLLM community. For example, we reveal that the shortcoming of counting capability greatly limits the compositional spatial capabilities of existing MLLMs. The evaluation code and benchmark datasets are available at https://github.com/Cuzyoung/SpaCE-10.

We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.

We present PlainMamba: a simple non-hierarchical state space model (SSM) designed for general visual recognition. The recent Mamba model has shown how SSMs can be highly competitive with other architectures on sequential data and initial attempts have been made to apply it to images. In this paper, we further adapt the selective scanning process of Mamba to the visual domain, enhancing its ability to learn features from two-dimensional images by (i) a continuous 2D scanning process that improves spatial continuity by ensuring adjacency of tokens in the scanning sequence, and (ii) direction-aware updating which enables the model to discern the spatial relations of tokens by encoding directional information. Our architecture is designed to be easy to use and easy to scale, formed by stacking identical PlainMamba blocks, resulting in a model with constant width throughout all layers. The architecture is further simplified by removing the need for special tokens. We evaluate PlainMamba on a variety of visual recognition tasks including image classification, semantic segmentation, object detection, and instance segmentation. Our method achieves performance gains over previous non-hierarchical models and is competitive with hierarchical alternatives. For tasks requiring high-resolution inputs, in particular, PlainMamba requires much less computing while maintaining high performance. Code and models are available at https://github.com/ChenhongyiYang/PlainMamba

Generative Large Multimodal Models (LMMs) like LLaVA and Qwen-VL excel at a wide variety of vision-language (VL) tasks such as image captioning or visual question answering. Despite strong performance, LMMs are not directly suited for foundational discriminative vision-language tasks (i.e., tasks requiring discrete label predictions) such as image classification and multiple-choice VQA. One key challenge in utilizing LMMs for discriminative tasks is the extraction of useful features from generative models. To overcome this issue, we propose an approach for finding features in the model's latent space to more effectively leverage LMMs for discriminative tasks. Toward this end, we present Sparse Attention Vectors (SAVs) -- a finetuning-free method that leverages sparse attention head activations (fewer than 1\% of the heads) in LMMs as strong features for VL tasks. With only few-shot examples, SAVs demonstrate state-of-the-art performance compared to a variety of few-shot and finetuned baselines on a collection of discriminative tasks. Our experiments also imply that SAVs can scale in performance with additional examples and generalize to similar tasks, establishing SAVs as both effective and robust multimodal feature representations.

Neural architecture search (NAS) finds high performing networks for a given task. Yet the results of NAS are fairly prosaic; they did not e.g. create a shift from convolutional structures to transformers. This is not least because the search spaces in NAS often aren't diverse enough to include such transformations a priori. Instead, for NAS to provide greater potential for fundamental design shifts, we need a novel expressive search space design which is built from more fundamental operations. To this end, we introduce einspace, a search space based on a parameterised probabilistic context-free grammar. Our space is versatile, supporting architectures of various sizes and complexities, while also containing diverse network operations which allow it to model convolutions, attention components and more. It contains many existing competitive architectures, and provides flexibility for discovering new ones. Using this search space, we perform experiments to find novel architectures as well as improvements on existing ones on the diverse Unseen NAS datasets. We show that competitive architectures can be obtained by searching from scratch, and we consistently find large improvements when initialising the search with strong baselines. We believe that this work is an important advancement towards a transformative NAS paradigm where search space expressivity and strategic search initialisation play key roles.

In an effort to create a more efficient AI system, we introduce a new multi-modality learning framework that leverages a modality-agnostic concept space possessing abstract knowledge and a set of modality-specific projection models tailored to process distinct modality inputs and map them onto the concept space. Decoupled from specific modalities and their associated projection models, the concept space focuses on learning abstract knowledge that is universally applicable across modalities. Subsequently, the knowledge embedded into the concept space streamlines the learning processes of modality-specific projection models. We evaluate our framework on two popular tasks: Image-Text Matching and Visual Question Answering. Our framework achieves performance on par with benchmark models while demonstrating more efficient learning curves.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NP- and #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

Object counting methods typically rely on manually annotated datasets. The cost of creating such datasets has restricted the versatility of these networks to count objects from specific classes (such as humans or penguins), and counting objects from diverse categories remains a challenge. The availability of robust text-to-image latent diffusion models (LDMs) raises the question of whether these models can be utilized to generate counting datasets. However, LDMs struggle to create images with an exact number of objects based solely on text prompts but they can be used to offer a dependable sorting signal by adding and removing objects within an image. Leveraging this data, we initially introduce an unsupervised sorting methodology to learn object-related features that are subsequently refined and anchored for counting purposes using counting data generated by LDMs. Further, we present a density classifier-guided method for dividing an image into patches containing objects that can be reliably counted. Consequently, we can generate counting data for any type of object and count them in an unsupervised manner. Our approach outperforms other unsupervised and few-shot alternatives and is not restricted to specific object classes for which counting data is available. Code to be released upon acceptance.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing image classifier and a semantic word embedding model, which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

Recent works have extended notions of feature importance to semantic concepts that are inherently interpretable to the users interacting with a black-box predictive model. Yet, precise statistical guarantees, such as false positive rate control, are needed to communicate findings transparently and to avoid unintended consequences in real-world scenarios. In this paper, we formalize the global (i.e., over a population) and local (i.e., for a sample) statistical importance of semantic concepts for the predictions of opaque models, by means of conditional independence, which allows for rigorous testing. We use recent ideas of sequential kernelized testing (SKIT) to induce a rank of importance across concepts, and showcase the effectiveness and flexibility of our framework on synthetic datasets as well as on image classification tasks using vision-language models such as CLIP.

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique. Code for our experiments can be found at github.com/edwardjhu/TP4.

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals p_d(y) can shift across domains but the class conditionals p(x|y) do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to p(d|x) suffices to identify p_d(y) and p_d(y|x) up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator p(d|x); (ii) discretize the data by clustering examples in p(d|x) space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered p(y|d) with the discriminator outputs p(d|x) to compute p_d(y|x) ; forall d. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve upon competitive unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.

Recent unsupervised domain adaptation methods have utilized vicinal space between the source and target domains. However, the equilibrium collapse of labels, a problem where the source labels are dominant over the target labels in the predictions of vicinal instances, has never been addressed. In this paper, we propose an instance-wise minimax strategy that minimizes the entropy of high uncertainty instances in the vicinal space to tackle the stated problem. We divide the vicinal space into two subspaces through the solution of the minimax problem: contrastive space and consensus space. In the contrastive space, inter-domain discrepancy is mitigated by constraining instances to have contrastive views and labels, and the consensus space reduces the confusion between intra-domain categories. The effectiveness of our method is demonstrated on public benchmarks, including Office-31, Office-Home, and VisDA-C, achieving state-of-the-art performances. We further show that our method outperforms the current state-of-the-art methods on PACS, which indicates that our instance-wise approach works well for multi-source domain adaptation as well. Code is available at https://github.com/NaJaeMin92/CoVi.

We investigate the space of weights spanned by a large collection of customized diffusion models. We populate this space by creating a dataset of over 60,000 models, each of which is a base model fine-tuned to insert a different person's visual identity. We model the underlying manifold of these weights as a subspace, which we term weights2weights. We demonstrate three immediate applications of this space -- sampling, editing, and inversion. First, as each point in the space corresponds to an identity, sampling a set of weights from it results in a model encoding a novel identity. Next, we find linear directions in this space corresponding to semantic edits of the identity (e.g., adding a beard). These edits persist in appearance across generated samples. Finally, we show that inverting a single image into this space reconstructs a realistic identity, even if the input image is out of distribution (e.g., a painting). Our results indicate that the weight space of fine-tuned diffusion models behaves as an interpretable latent space of identities.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product of training large language models (LLMs). One major drawback of this type of representation is their incomprehensibility to humans. Understanding the embedding space is crucial for several important needs, including the need to debug the embedding method and compare it to alternatives, and the need to detect biases hidden in the model. In this paper, we present a novel method of understanding embeddings by transforming a latent embedding space into a comprehensible conceptual space. We present an algorithm for deriving a conceptual space with dynamic on-demand granularity. We devise a new evaluation method, using either human rater or LLM-based raters, to show that the conceptualized vectors indeed represent the semantics of the original latent ones. We show the use of our method for various tasks, including comparing the semantics of alternative models and tracing the layers of the LLM. The code is available online https://github.com/adiSimhi/Interpreting-Embedding-Spaces-by-Conceptualization.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

The goal of this paper is to improve the generality and accuracy of open-vocabulary object counting in images. To improve the generality, we repurpose an open-vocabulary detection foundation model (GroundingDINO) for the counting task, and also extend its capabilities by introducing modules to enable specifying the target object to count by visual exemplars. In turn, these new capabilities - being able to specify the target object by multi-modalites (text and exemplars) - lead to an improvement in counting accuracy. We make three contributions: First, we introduce the first open-world counting model, CountGD, where the prompt can be specified by a text description or visual exemplars or both; Second, we show that the performance of the model significantly improves the state of the art on multiple counting benchmarks - when using text only, CountGD is comparable to or outperforms all previous text-only works, and when using both text and visual exemplars, we outperform all previous models; Third, we carry out a preliminary study into different interactions between the text and visual exemplar prompts, including the cases where they reinforce each other and where one restricts the other. The code and an app to test the model are available at https://www.robots.ox.ac.uk/~vgg/research/countgd/.

We present a new dataset, Functional Map of the World (fMoW), which aims to inspire the development of machine learning models capable of predicting the functional purpose of buildings and land use from temporal sequences of satellite images and a rich set of metadata features. The metadata provided with each image enables reasoning about location, time, sun angles, physical sizes, and other features when making predictions about objects in the image. Our dataset consists of over 1 million images from over 200 countries. For each image, we provide at least one bounding box annotation containing one of 63 categories, including a "false detection" category. We present an analysis of the dataset along with baseline approaches that reason about metadata and temporal views. Our data, code, and pretrained models have been made publicly available.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

In this work we introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group SE(d). We propose an equivariant attention mechanism that operates on features extracted by steerable convolutions. Operating in Fourier space, our network utilizes Fourier space non-linearities. Our experiments in both two and three dimensions show that adding a steerable transformer encoder layer to a steerable convolution network enhances performance.

A key aspect of text-to-image personalization methods is the manner in which the target concept is represented within the generative process. This choice greatly affects the visual fidelity, downstream editability, and disk space needed to store the learned concept. In this paper, we explore a new text-conditioning space that is dependent on both the denoising process timestep (time) and the denoising U-Net layers (space) and showcase its compelling properties. A single concept in the space-time representation is composed of hundreds of vectors, one for each combination of time and space, making this space challenging to optimize directly. Instead, we propose to implicitly represent a concept in this space by optimizing a small neural mapper that receives the current time and space parameters and outputs the matching token embedding. In doing so, the entire personalized concept is represented by the parameters of the learned mapper, resulting in a compact, yet expressive, representation. Similarly to other personalization methods, the output of our neural mapper resides in the input space of the text encoder. We observe that one can significantly improve the convergence and visual fidelity of the concept by introducing a textual bypass, where our neural mapper additionally outputs a residual that is added to the output of the text encoder. Finally, we show how one can impose an importance-based ordering over our implicit representation, providing users control over the reconstruction and editability of the learned concept using a single trained model. We demonstrate the effectiveness of our approach over a range of concepts and prompts, showing our method's ability to generate high-quality and controllable compositions without fine-tuning any parameters of the generative model itself.

Selecting appropriate datasets is critical in modern computer vision. However, no general-purpose tools exist to evaluate the extent to which two datasets differ. For this, we propose representing images - and by extension datasets - using Distributions of Neuron Activations (DNAs). DNAs fit distributions, such as histograms or Gaussians, to activations of neurons in a pre-trained feature extractor through which we pass the image(s) to represent. This extractor is frozen for all datasets, and we rely on its generally expressive power in feature space. By comparing two DNAs, we can evaluate the extent to which two datasets differ with granular control over the comparison attributes of interest, providing the ability to customise the way distances are measured to suit the requirements of the task at hand. Furthermore, DNAs are compact, representing datasets of any size with less than 15 megabytes. We demonstrate the value of DNAs by evaluating their applicability on several tasks, including conditional dataset comparison, synthetic image evaluation, and transfer learning, and across diverse datasets, ranging from synthetic cat images to celebrity faces and urban driving scenes.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Transformer and its variants are fundamental neural architectures in deep learning. Recent works show that learning attention in the Fourier space can improve the long sequence learning capability of Transformers. We argue that wavelet transform shall be a better choice because it captures both position and frequency information with linear time complexity. Therefore, in this paper, we systematically study the synergy between wavelet transform and Transformers. We propose Wavelet Space Attention (WavSpA) that facilitates attention learning in a learnable wavelet coefficient space which replaces the attention in Transformers by (1) applying forward wavelet transform to project the input sequences to multi-resolution bases, (2) conducting attention learning in the wavelet coefficient space, and (3) reconstructing the representation in input space via backward wavelet transform. Extensive experiments on the Long Range Arena demonstrate that learning attention in the wavelet space using either fixed or adaptive wavelets can consistently improve Transformer's performance and also significantly outperform learning in Fourier space. We further show our method can enhance Transformer's reasoning extrapolation capability over distance on the LEGO chain-of-reasoning task.

Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily focus on how to search feature interaction in a coarse-grained space, less attention has been given to a finer granularity. In this work, we introduce a hybrid-grained feature interaction selection approach that targets both feature field and feature value for deep sparse networks. To explore such expansive space, we propose a decomposed space which is calculated on the fly. We then develop a selection algorithm called OptFeature, which efficiently selects the feature interaction from both the feature field and the feature value simultaneously. Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

Large vision-language models (VLMs) are shown to learn rich joint image-text representations enabling high performances in relevant downstream tasks. However, they fail to showcase their quantitative understanding of objects, and they lack good counting-aware representation. This paper conducts a reproducibility study of 'Teaching CLIP to Count to Ten' (Paiss et al., 2023), which presents a method to finetune a CLIP model (Radford et al., 2021) to improve zero-shot counting accuracy in an image while maintaining the performance for zero-shot classification by introducing a counting-contrastive loss term. We improve the model's performance on a smaller subset of their training data with lower computational resources. We verify these claims by reproducing their study with our own code. The implementation can be found at https://github.com/SforAiDl/CountCLIP.

Class-Incremental Learning (CIL) requires a learning system to continually learn new classes without forgetting. Despite the strong performance of Pre-Trained Models (PTMs) in CIL, a critical issue persists: learning new classes often results in the overwriting of old ones. Excessive modification of the network causes forgetting, while minimal adjustments lead to an inadequate fit for new classes. As a result, it is desired to figure out a way of efficient model updating without harming former knowledge. In this paper, we propose ExpAndable Subspace Ensemble (EASE) for PTM-based CIL. To enable model updating without conflict, we train a distinct lightweight adapter module for each new task, aiming to create task-specific subspaces. These adapters span a high-dimensional feature space, enabling joint decision-making across multiple subspaces. As data evolves, the expanding subspaces render the old class classifiers incompatible with new-stage spaces. Correspondingly, we design a semantic-guided prototype complement strategy that synthesizes old classes' new features without using any old class instance. Extensive experiments on seven benchmark datasets verify EASE's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/CVPR24-Ease

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Contrastive learning, a prominent approach to representation learning, traditionally assumes positive pairs are closely related samples (the same image or class) and negative pairs are distinct samples. We challenge this assumption by proposing to learn from arbitrary pairs, allowing any pair of samples to be positive within our framework.The primary challenge of the proposed approach lies in applying contrastive learning to disparate pairs which are semantically distant. Motivated by the discovery that SimCLR can separate given arbitrary pairs (e.g., garter snake and table lamp) in a subspace, we propose a feature filter in the condition of class pairs that creates the requisite subspaces by gate vectors selectively activating or deactivating dimensions. This filter can be optimized through gradient descent within a conventional contrastive learning mechanism. We present Hydra, a universal contrastive learning framework for visual representations that extends conventional contrastive learning to accommodate arbitrary pairs. Our approach is validated using IN1K, where 1K diverse classes compose 500,500 pairs, most of them being distinct. Surprisingly, Hydra achieves superior performance in this challenging setting. Additional benefits include the prevention of dimensional collapse and the discovery of class relationships. Our work highlights the value of learning common features of arbitrary pairs and potentially broadens the applicability of contrastive learning techniques on the sample pairs with weak relationships.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality.

We propose prototypical networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each new class. Prototypical networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class. Compared to recent approaches for few-shot learning, they reflect a simpler inductive bias that is beneficial in this limited-data regime, and achieve excellent results. We provide an analysis showing that some simple design decisions can yield substantial improvements over recent approaches involving complicated architectural choices and meta-learning. We further extend prototypical networks to zero-shot learning and achieve state-of-the-art results on the CU-Birds dataset.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

Recent advances in foundation models present new opportunities for interpretable visual recognition -- one can first query Large Language Models (LLMs) to obtain a set of attributes that describe each class, then apply vision-language models to classify images via these attributes. Pioneering work shows that querying thousands of attributes can achieve performance competitive with image features. However, our further investigation on 8 datasets reveals that LLM-generated attributes in a large quantity perform almost the same as random words. This surprising finding suggests that significant noise may be present in these attributes. We hypothesize that there exist subsets of attributes that can maintain the classification performance with much smaller sizes, and propose a novel learning-to-search method to discover those concise sets of attributes. As a result, on the CUB dataset, our method achieves performance close to that of massive LLM-generated attributes (e.g., 10k attributes for CUB), yet using only 32 attributes in total to distinguish 200 bird species. Furthermore, our new paradigm demonstrates several additional benefits: higher interpretability and interactivity for humans, and the ability to summarize knowledge for a recognition task.

Recent studies suggest that deep learning models inductive bias towards favoring simpler features may be one of the sources of shortcut learning. Yet, there has been limited focus on understanding the complexity of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features, represented as directions in the penultimate layer, that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity and find a spectrum of simple to complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features flow, and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features complexity and their importance in driving the networks decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a sedimentation process, allowing the model to build upon these foundational elements.

Visual Place Recognition (VPR) is a crucial component of many visual localization pipelines for embodied agents. VPR is often formulated as an image retrieval task aimed at jointly learning local features and an aggregation method. The current state-of-the-art VPR methods rely on VLAD aggregation, which can be trained to learn a weighted contribution of features through their soft assignment to cluster centers. However, this process has two key limitations. Firstly, the feature-to-cluster weighting does not account for over-represented repetitive structures within a cluster, e.g., shadows or window panes; this phenomenon is also referred to as the `burstiness' problem, classically solved by discounting repetitive features before aggregation. Secondly, feature to cluster comparisons are compute-intensive for state-of-the-art image encoders with high-dimensional local features. This paper addresses these limitations by introducing VLAD-BuFF with two novel contributions: i) a self-similarity based feature discounting mechanism to learn Burst-aware features within end-to-end VPR training, and ii) Fast Feature aggregation by reducing local feature dimensions specifically through PCA-initialized learnable pre-projection. We benchmark our method on 9 public datasets, where VLAD-BuFF sets a new state of the art. Our method is able to maintain its high recall even for 12x reduced local feature dimensions, thus enabling fast feature aggregation without compromising on recall. Through additional qualitative studies, we show how our proposed weighting method effectively downweights the non-distinctive features. Source code: https://github.com/Ahmedest61/VLAD-BuFF/.

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training sophisticated deep networks on large numbers of relatively unprocessed inputs (so-called automated feature engineering), for many tasks in physics, sets of theoretically well-motivated and well-understood features already exist. Working with such features can bring many benefits, including greater interpretability, reduced training and run time, and enhanced stability and robustness. We develop a new feature selection method based on Distance Correlation (DisCo), and demonstrate its effectiveness on the tasks of boosted top- and W-tagging. Using our method to select features from a set of over 7,000 energy flow polynomials, we show that we can match the performance of much deeper architectures, by using only ten features and two orders-of-magnitude fewer model parameters.

Vision Transformers achieved outstanding performance in many computer vision tasks. Early Vision Transformers such as ViT and DeiT adopt global self-attention, which is computationally expensive when the number of patches is large. To improve efficiency, recent Vision Transformers adopt local self-attention mechanisms, where self-attention is computed within local windows. Despite the fact that window-based local self-attention significantly boosts efficiency, it fails to capture the relationships between distant but similar patches in the image plane. To overcome this limitation of image-space local attention, in this paper, we further exploit the locality of patches in the feature space. We group the patches into multiple clusters using their features, and self-attention is computed within every cluster. Such feature-space local attention effectively captures the connections between patches across different local windows but still relevant. We propose a Bilateral lOcal Attention vision Transformer (BOAT), which integrates feature-space local attention with image-space local attention. We further integrate BOAT with both Swin and CSWin models, and extensive experiments on several benchmark datasets demonstrate that our BOAT-CSWin model clearly and consistently outperforms existing state-of-the-art CNN models and vision Transformers.

Large vision-language models (VLMs), such as CLIP, learn rich joint image-text representations, facilitating advances in numerous downstream tasks, including zero-shot classification and text-to-image generation. Nevertheless, existing VLMs exhibit a prominent well-documented limitation - they fail to encapsulate compositional concepts such as counting. We introduce a simple yet effective method to improve the quantitative understanding of VLMs, while maintaining their overall performance on common benchmarks. Specifically, we propose a new counting-contrastive loss used to finetune a pre-trained VLM in tandem with its original objective. Our counting loss is deployed over automatically-created counterfactual examples, each consisting of an image and a caption containing an incorrect object count. For example, an image depicting three dogs is paired with the caption "Six dogs playing in the yard". Our loss encourages discrimination between the correct caption and its counterfactual variant which serves as a hard negative example. To the best of our knowledge, this work is the first to extend CLIP's capabilities to object counting. Furthermore, we introduce "CountBench" - a new image-text counting benchmark for evaluating a model's understanding of object counting. We demonstrate a significant improvement over state-of-the-art baseline models on this task. Finally, we leverage our count-aware CLIP model for image retrieval and text-conditioned image generation, demonstrating that our model can produce specific counts of objects more reliably than existing ones.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a batch-style correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them empirically on image, speech, and text tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). We also explore a stochastic optimization procedure for minibatch correlation-based objectives and discuss the time/performance trade-offs for kernel-based and neural network-based implementations.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but limited understanding of the strengths and weaknesses of these models, and the table representations they generate, makes the process of finding a suitable model for a given task reliant on trial and error. There is an urgent need to gain a comprehensive understanding of these models to minimize inefficiency and failures in downstream usage. To address this need, we propose Observatory, a formal framework to systematically analyze embedding representations of relational tables. Motivated both by invariants of the relational data model and by statistical considerations regarding data distributions, we define eight primitive properties, and corresponding measures to quantitatively characterize table embeddings for these properties. Based on these properties, we define an extensible framework to evaluate language and table embedding models. We collect and synthesize a suite of datasets and use Observatory to analyze nine such models. Our analysis provides insights into the strengths and weaknesses of learned representations over tables. We find, for example, that some models are sensitive to table structure such as column order, that functional dependencies are rarely reflected in embeddings, and that specialized table embedding models have relatively lower sample fidelity. Such insights help researchers and practitioners better anticipate model behaviors and select appropriate models for their downstream tasks, while guiding researchers in the development of new models.

Music two-tower multimodal systems integrate audio and text modalities into a joint audio-text space, enabling direct comparison between songs and their corresponding labels. These systems enable new approaches for classification and retrieval, leveraging both modalities. Despite the promising results they have shown for zero-shot classification and retrieval tasks, closer inspection of the embeddings is needed. This paper evaluates the inherent zero-shot properties of joint audio-text spaces for the case-study of instrument recognition. We present an evaluation and analysis of two-tower systems for zero-shot instrument recognition and a detailed analysis of the properties of the pre-joint and joint embeddings spaces. Our findings suggest that audio encoders alone demonstrate good quality, while challenges remain within the text encoder or joint space projection. Specifically, two-tower systems exhibit sensitivity towards specific words, favoring generic prompts over musically informed ones. Despite the large size of textual encoders, they do not yet leverage additional textual context or infer instruments accurately from their descriptions. Lastly, a novel approach for quantifying the semantic meaningfulness of the textual space leveraging an instrument ontology is proposed. This method reveals deficiencies in the systems' understanding of instruments and provides evidence of the need for fine-tuning text encoders on musical data.

In this study, we introduce FEET, a standardized protocol designed to guide the development and benchmarking of foundation models. While numerous benchmark datasets exist for evaluating these models, we propose a structured evaluation protocol across three distinct scenarios to gain a comprehensive understanding of their practical performance. We define three primary use cases: frozen embeddings, few-shot embeddings, and fully fine-tuned embeddings. Each scenario is detailed and illustrated through two case studies: one in sentiment analysis and another in the medical domain, demonstrating how these evaluations provide a thorough assessment of foundation models' effectiveness in research applications. We recommend this protocol as a standard for future research aimed at advancing representation learning models.

Recent progress has been made towards learning invariant or equivariant representations with self-supervised learning. While invariant methods are evaluated on large scale datasets, equivariant ones are evaluated in smaller, more controlled, settings. We aim at bridging the gap between the two in order to learn more diverse representations that are suitable for a wide range of tasks. We start by introducing a dataset called 3DIEBench, consisting of renderings from 3D models over 55 classes and more than 2.5 million images where we have full control on the transformations applied to the objects. We further introduce a predictor architecture based on hypernetworks to learn equivariant representations with no possible collapse to invariance. We introduce SIE (Split Invariant-Equivariant) which combines the hypernetwork-based predictor with representations split in two parts, one invariant, the other equivariant, to learn richer representations. We demonstrate significant performance gains over existing methods on equivariance related tasks from both a qualitative and quantitative point of view. We further analyze our introduced predictor and show how it steers the learned latent space. We hope that both our introduced dataset and approach will enable learning richer representations without supervision in more complex scenarios. Code and data are available at https://github.com/facebookresearch/SIE.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

Semantic segmentation usually suffers from a long-tail data distribution. Due to the imbalanced number of samples across categories, the features of those tail classes may get squeezed into a narrow area in the feature space. Towards a balanced feature distribution, we introduce category-wise variation into the network predictions in the training phase such that an instance is no longer projected to a feature point, but a small region instead. Such a perturbation is highly dependent on the category scale, which appears as assigning smaller variation to head classes and larger variation to tail classes. In this way, we manage to close the gap between the feature areas of different categories, resulting in a more balanced representation. It is noteworthy that the introduced variation is discarded at the inference stage to facilitate a confident prediction. Although with an embarrassingly simple implementation, our method manifests itself in strong generalizability to various datasets and task settings. Extensive experiments suggest that our plug-in design lends itself well to a range of state-of-the-art approaches and boosts the performance on top of them.

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest, and optimizes an Empirical Risk Minimization objective. However, Empirical Risk Minimization is known to suffer from distributional shifts which hurt generalizability to prompts unseen during training. By leveraging the regularization ability of Bayesian methods, we frame prompt learning from the Bayesian perspective and formulate it as a variational inference problem. Our approach regularizes the prompt space, reduces overfitting to the seen prompts and improves the prompt generalization on unseen prompts. Our framework is implemented by modeling the input prompt space in a probabilistic manner, as an a priori distribution which makes our proposal compatible with prompt learning approaches that are unconditional or conditional on the image. We demonstrate empirically on 15 benchmarks that Bayesian prompt learning provides an appropriate coverage of the prompt space, prevents learning spurious features, and exploits transferable invariant features. This results in better generalization of unseen prompts, even across different datasets and domains. Code available at: https://github.com/saic-fi/Bayesian-Prompt-Learning

Zero-shot object counting (ZOC) aims to enumerate objects in images using only the names of object classes during testing, without the need for manual annotations. However, a critical challenge in current ZOC methods lies in their inability to identify high-quality exemplars effectively. This deficiency hampers scalability across diverse classes and undermines the development of strong visual associations between the identified classes and image content. To this end, we propose the Visual Association-based Zero-shot Object Counting (VA-Count) framework. VA-Count consists of an Exemplar Enhancement Module (EEM) and a Noise Suppression Module (NSM) that synergistically refine the process of class exemplar identification while minimizing the consequences of incorrect object identification. The EEM utilizes advanced vision-language pretaining models to discover potential exemplars, ensuring the framework's adaptability to various classes. Meanwhile, the NSM employs contrastive learning to differentiate between optimal and suboptimal exemplar pairs, reducing the negative effects of erroneous exemplars. VA-Count demonstrates its effectiveness and scalability in zero-shot contexts with superior performance on two object counting datasets.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Automated interpretability research aims to identify concepts encoded in neural network features to enhance human understanding of model behavior. Current feature description methods face two critical challenges: limited robustness and the flawed assumption that each neuron encodes only a single concept (monosemanticity), despite growing evidence that neurons are often polysemantic. This assumption restricts the expressiveness of feature descriptions and limits their ability to capture the full range of behaviors encoded in model internals. To address this, we introduce Polysemantic FeatuRe Identification and Scoring Method (PRISM), a novel framework that captures the inherent complexity of neural network features. Unlike prior approaches that assign a single description per feature, PRISM provides more nuanced descriptions for both polysemantic and monosemantic features. We apply PRISM to language models and, through extensive benchmarking against existing methods, demonstrate that our approach produces more accurate and faithful feature descriptions, improving both overall description quality (via a description score) and the ability to capture distinct concepts when polysemanticity is present (via a polysemanticity score).

Most counting questions in visual question answering (VQA) datasets are simple and require no more than object detection. Here, we study algorithms for complex counting questions that involve relationships between objects, attribute identification, reasoning, and more. To do this, we created TallyQA, the world's largest dataset for open-ended counting. We propose a new algorithm for counting that uses relation networks with region proposals. Our method lets relation networks be efficiently used with high-resolution imagery. It yields state-of-the-art results compared to baseline and recent systems on both TallyQA and the HowMany-QA benchmark.

Class-agnostic counting methods enumerate objects of an arbitrary class, providing tremendous utility in many fields. Prior works have limited usefulness as they require either a set of examples of the type to be counted or that the query image contains only a single type of object. A significant factor in these shortcomings is the lack of a dataset to properly address counting in settings with more than one kind of object present. To address these issues, we propose the first Multi-class, Class-Agnostic Counting dataset (MCAC) and A Blind Counter (ABC123), a method that can count multiple types of objects simultaneously without using examples of type during training or inference. ABC123 introduces a new paradigm where instead of requiring exemplars to guide the enumeration, examples are found after the counting stage to help a user understand the generated outputs. We show that ABC123 outperforms contemporary methods on MCAC without needing human in-the-loop annotations. We also show that this performance transfers to FSC-147, the standard class-agnostic counting dataset. MCAC is available at MCAC.active.vision and ABC123 is available at ABC123.active.vision.

Different from human nature, it is still common practice today for vision tasks to train deep learning models only initially and on fixed datasets. A variety of approaches have recently addressed handling continual data streams. However, extending these methods to manage out-of-distribution (OOD) scenarios has not effectively been investigated. On the other hand, it has recently been shown that non-continual neural mesh models exhibit strong performance in generalizing to such OOD scenarios. To leverage this decisive property in a continual learning setting, we propose incremental neural mesh models that can be extended with new meshes over time. In addition, we present a latent space initialization strategy that enables us to allocate feature space for future unseen classes in advance and a positional regularization term that forces the features of the different classes to consistently stay in respective latent space regions. We demonstrate the effectiveness of our method through extensive experiments on the Pascal3D and ObjectNet3D datasets and show that our approach outperforms the baselines for classification by 2-6% in the in-domain and by 6-50% in the OOD setting. Our work also presents the first incremental learning approach for pose estimation. Our code and model can be found at https://github.com/Fischer-Tom/iNeMo.

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

We consider low-shot counting of arbitrary semantic categories in the image using only few annotated exemplars (few-shot) or no exemplars (no-shot). The standard few-shot pipeline follows extraction of appearance queries from exemplars and matching them with image features to infer the object counts. Existing methods extract queries by feature pooling, but neglect the shape information (e.g., size and aspect), which leads to a reduced object localization accuracy and count estimates. We propose a Low-shot Object Counting network with iterative prototype Adaptation (LOCA). Our main contribution is the new object prototype extraction module, which iteratively fuses the exemplar shape and appearance queries with image features. The module is easily adapted to zero-shot scenario, enabling LOCA to cover the entire spectrum of low-shot counting problems. LOCA outperforms all recent state-of-the-art methods on FSC147 benchmark by 20-30% in RMSE on one-shot and few-shot and achieves state-of-the-art on zero-shot scenarios, while demonstrating better generalization capabilities.

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, e.g., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in https://github.com/wdayang/Manifoldron for free download and evaluation.

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.

Progress on object detection is enabled by datasets that focus the research community's attention on open challenges. This process led us from simple images to complex scenes and from bounding boxes to segmentation masks. In this work, we introduce LVIS (pronounced `el-vis'): a new dataset for Large Vocabulary Instance Segmentation. We plan to collect ~2 million high-quality instance segmentation masks for over 1000 entry-level object categories in 164k images. Due to the Zipfian distribution of categories in natural images, LVIS naturally has a long tail of categories with few training samples. Given that state-of-the-art deep learning methods for object detection perform poorly in the low-sample regime, we believe that our dataset poses an important and exciting new scientific challenge. LVIS is available at http://www.lvisdataset.org.

Disentangling model activations into meaningful features is a central problem in interpretability. However, the absence of ground-truth for these features in realistic scenarios makes validating recent approaches, such as sparse dictionary learning, elusive. To address this challenge, we propose a framework for evaluating feature dictionaries in the context of specific tasks, by comparing them against supervised feature dictionaries. First, we demonstrate that supervised dictionaries achieve excellent approximation, control, and interpretability of model computations on the task. Second, we use the supervised dictionaries to develop and contextualize evaluations of unsupervised dictionaries along the same three axes. We apply this framework to the indirect object identification (IOI) task using GPT-2 Small, with sparse autoencoders (SAEs) trained on either the IOI or OpenWebText datasets. We find that these SAEs capture interpretable features for the IOI task, but they are less successful than supervised features in controlling the model. Finally, we observe two qualitative phenomena in SAE training: feature occlusion (where a causally relevant concept is robustly overshadowed by even slightly higher-magnitude ones in the learned features), and feature over-splitting (where binary features split into many smaller, less interpretable features). We hope that our framework will provide a useful step towards more objective and grounded evaluations of sparse dictionary learning methods.

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

Zero-shot learning (ZSL) models rely on learning a joint embedding space where both textual/semantic description of object classes and visual representation of object images can be projected to for nearest neighbour search. Despite the success of deep neural networks that learn an end-to-end model between text and images in other vision problems such as image captioning, very few deep ZSL model exists and they show little advantage over ZSL models that utilise deep feature representations but do not learn an end-to-end embedding. In this paper we argue that the key to make deep ZSL models succeed is to choose the right embedding space. Instead of embedding into a semantic space or an intermediate space, we propose to use the visual space as the embedding space. This is because that in this space, the subsequent nearest neighbour search would suffer much less from the hubness problem and thus become more effective. This model design also provides a natural mechanism for multiple semantic modalities (e.g., attributes and sentence descriptions) to be fused and optimised jointly in an end-to-end manner. Extensive experiments on four benchmarks show that our model significantly outperforms the existing models. Code is available at https://github.com/lzrobots/DeepEmbeddingModel_ZSL

Can we automatically group images into semantically meaningful clusters when ground-truth annotations are absent? The task of unsupervised image classification remains an important, and open challenge in computer vision. Several recent approaches have tried to tackle this problem in an end-to-end fashion. In this paper, we deviate from recent works, and advocate a two-step approach where feature learning and clustering are decoupled. First, a self-supervised task from representation learning is employed to obtain semantically meaningful features. Second, we use the obtained features as a prior in a learnable clustering approach. In doing so, we remove the ability for cluster learning to depend on low-level features, which is present in current end-to-end learning approaches. Experimental evaluation shows that we outperform state-of-the-art methods by large margins, in particular +26.6% on CIFAR10, +25.0% on CIFAR100-20 and +21.3% on STL10 in terms of classification accuracy. Furthermore, our method is the first to perform well on a large-scale dataset for image classification. In particular, we obtain promising results on ImageNet, and outperform several semi-supervised learning methods in the low-data regime without the use of any ground-truth annotations. The code is made publicly available at https://github.com/wvangansbeke/Unsupervised-Classification.

Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by Wang2020UnderstandingCR introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at https://github.com/sunset-clouds/WassersteinUniformityMetric.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Few shot classification aims to learn to recognize novel categories using only limited samples per category. Most current few shot methods use a base dataset rich in labeled examples to train an encoder that is used for obtaining representations of support instances for novel classes. Since the test instances are from a distribution different to the base distribution, their feature representations are of poor quality, degrading performance. In this paper we propose to make use of the well-trained feature representations of the base dataset that are closest to each support instance to improve its representation during meta-test time. To this end, we propose BaseTransformers, that attends to the most relevant regions of the base dataset feature space and improves support instance representations. Experiments on three benchmark data sets show that our method works well for several backbones and achieves state-of-the-art results in the inductive one shot setting. Code is available at github.com/mayug/BaseTransformers

Real-world scenarios are usually accompanied by continuously appearing classes with scare labeled samples, which require the machine learning model to incrementally learn new classes and maintain the knowledge of base classes. In this Few-Shot Class-Incremental Learning (FSCIL) scenario, existing methods either introduce extra learnable components or rely on a frozen feature extractor to mitigate catastrophic forgetting and overfitting problems. However, we find a tendency for existing methods to misclassify the samples of new classes into base classes, which leads to the poor performance of new classes. In other words, the strong discriminability of base classes distracts the classification of new classes. To figure out this intriguing phenomenon, we observe that although the feature extractor is only trained on base classes, it can surprisingly represent the semantic similarity between the base and unseen new classes. Building upon these analyses, we propose a simple yet effective Training-frEE calibratioN (TEEN) strategy to enhance the discriminability of new classes by fusing the new prototypes (i.e., mean features of a class) with weighted base prototypes. In addition to standard benchmarks in FSCIL, TEEN demonstrates remarkable performance and consistent improvements over baseline methods in the few-shot learning scenario. Code is available at: https://github.com/wangkiw/TEEN

Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a O(Nlog N) memory footprint for a length N sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

The recent breakthroughs in natural language processing for model pretraining on large quantities of data have opened the way for similar foundation models in computer vision. These models could greatly simplify the use of images in any system by producing all-purpose visual features, i.e., features that work across image distributions and tasks without finetuning. This work shows that existing pretraining methods, especially self-supervised methods, can produce such features if trained on enough curated data from diverse sources. We revisit existing approaches and combine different techniques to scale our pretraining in terms of data and model size. Most of the technical contributions aim at accelerating and stabilizing the training at scale. In terms of data, we propose an automatic pipeline to build a dedicated, diverse, and curated image dataset instead of uncurated data, as typically done in the self-supervised literature. In terms of models, we train a ViT model (Dosovitskiy et al., 2020) with 1B parameters and distill it into a series of smaller models that surpass the best available all-purpose features, OpenCLIP (Ilharco et al., 2021) on most of the benchmarks at image and pixel levels.

Object counting is pivotal for understanding the composition of scenes. Previously, this task was dominated by class-specific methods, which have gradually evolved into more adaptable class-agnostic strategies. However, these strategies come with their own set of limitations, such as the need for manual exemplar input and multiple passes for multiple categories, resulting in significant inefficiencies. This paper introduces a new, more practical approach enabling simultaneous counting of multiple object categories using an open vocabulary framework. Our solution, OmniCount, stands out by using semantic and geometric insights from pre-trained models to count multiple categories of objects as specified by users, all without additional training. OmniCount distinguishes itself by generating precise object masks and leveraging point prompts via the Segment Anything Model for efficient counting. To evaluate OmniCount, we created the OmniCount-191 benchmark, a first-of-its-kind dataset with multi-label object counts, including points, bounding boxes, and VQA annotations. Our comprehensive evaluation in OmniCount-191, alongside other leading benchmarks, demonstrates OmniCount's exceptional performance, significantly outpacing existing solutions and heralding a new era in object counting technology.

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND. Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on a variety of multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 action recognition, and ERA5 weather forecasting.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

Foundation models trained at scale exhibit remarkable emergent behaviors, learning new capabilities beyond their initial training objectives. We find such emergent behaviors in biological vision models via large-scale contrastive vision-language training. To achieve this, we first curate TreeOfLife-200M, comprising 214 million images of living organisms, the largest and most diverse biological organism image dataset to date. We then train BioCLIP 2 on TreeOfLife-200M to distinguish different species. Despite the narrow training objective, BioCLIP 2 yields extraordinary accuracy when applied to various biological visual tasks such as habitat classification and trait prediction. We identify emergent properties in the learned embedding space of BioCLIP 2. At the inter-species level, the embedding distribution of different species aligns closely with functional and ecological meanings (e.g., beak sizes and habitats). At the intra-species level, instead of being diminished, the intra-species variations (e.g., life stages and sexes) are preserved and better separated in subspaces orthogonal to inter-species distinctions. We provide formal proof and analyses to explain why hierarchical supervision and contrastive objectives encourage these emergent properties. Crucially, our results reveal that these properties become increasingly significant with larger-scale training data, leading to a biologically meaningful embedding space.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

Many machine learning algorithms require the input to be represented as a fixed-length feature vector. When it comes to texts, one of the most common fixed-length features is bag-of-words. Despite their popularity, bag-of-words features have two major weaknesses: they lose the ordering of the words and they also ignore semantics of the words. For example, "powerful," "strong" and "Paris" are equally distant. In this paper, we propose Paragraph Vector, an unsupervised algorithm that learns fixed-length feature representations from variable-length pieces of texts, such as sentences, paragraphs, and documents. Our algorithm represents each document by a dense vector which is trained to predict words in the document. Its construction gives our algorithm the potential to overcome the weaknesses of bag-of-words models. Empirical results show that Paragraph Vectors outperform bag-of-words models as well as other techniques for text representations. Finally, we achieve new state-of-the-art results on several text classification and sentiment analysis tasks.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

We introduce a novel approach for keypoint detection task that combines handcrafted and learned CNN filters within a shallow multi-scale architecture. Handcrafted filters provide anchor structures for learned filters, which localize, score and rank repeatable features. Scale-space representation is used within the network to extract keypoints at different levels. We design a loss function to detect robust features that exist across a range of scales and to maximize the repeatability score. Our Key.Net model is trained on data synthetically created from ImageNet and evaluated on HPatches benchmark. Results show that our approach outperforms state-of-the-art detectors in terms of repeatability, matching performance and complexity.

Deep learning models have become increasingly useful in many different industries. On the domain of image classification, convolutional neural networks proved the ability to learn robust features for the closed set problem, as shown in many different datasets, such as MNIST FASHIONMNIST, CIFAR10, CIFAR100, and IMAGENET. These approaches use deep neural networks with dense layers with softmax activation functions in order to learn features that can separate classes in a latent space. However, this traditional approach is not useful for identifying classes unseen on the training set, known as the open set problem. A similar problem occurs in scenarios involving learning on small data. To tackle both problems, few-shot learning has been proposed. In particular, metric learning learns features that obey constraints of a metric distance in the latent space in order to perform classification. However, while this approach proves to be useful for the open set problem, current implementation requires pair-wise training, where both positive and negative examples of similar images are presented during the training phase, which limits the applicability of these approaches in large data or large class scenarios given the combinatorial nature of the possible inputs.In this paper, we present a constraint-based approach applied to the representations in the latent space under the normalized softmax loss, proposed by[18]. We experimentally validate the proposed approach for the classification of unseen classes on different datasets using both metric learning and the normalized softmax loss, on disjoint and joint scenarios. Our results show that not only our proposed strategy can be efficiently trained on larger set of classes, as it does not require pairwise learning, but also present better classification results than the metric learning strategies surpassing its accuracy by a significant margin.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Machine learning models will often fail when deployed in an environment with a data distribution that is different than the training distribution. When multiple environments are available during training, many methods exist that learn representations which are invariant across the different distributions, with the hope that these representations will be transportable to unseen domains. In this work, we present a nonparametric strategy for learning invariant representations based on the recently-proposed Nadaraya-Watson (NW) head. The NW head makes a prediction by comparing the learned representations of the query to the elements of a support set that consists of labeled data. We demonstrate that by manipulating the support set, one can encode different causal assumptions. In particular, restricting the support set to a single environment encourages the model to learn invariant features that do not depend on the environment. We present a causally-motivated setup for our modeling and training strategy and validate on three challenging real-world domain generalization tasks in computer vision.

With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric prediction. In this paper, we provide one of the first comprehensive investigations into embedding-based regression and demonstrate that LLM embeddings as features can be better for high-dimensional regression tasks than using traditional feature engineering. This regression performance can be explained in part due to LLM embeddings over numeric data inherently preserving Lipschitz continuity over the feature space. Furthermore, we quantify the contribution of different model effects, most notably model size and language understanding, which we find surprisingly do not always improve regression performance.

We address the problem of class incremental learning, which is a core step towards achieving adaptive vision intelligence. In particular, we consider the task setting of incremental learning with limited memory and aim to achieve better stability-plasticity trade-off. To this end, we propose a novel two-stage learning approach that utilizes a dynamically expandable representation for more effective incremental concept modeling. Specifically, at each incremental step, we freeze the previously learned representation and augment it with additional feature dimensions from a new learnable feature extractor. This enables us to integrate new visual concepts with retaining learned knowledge. We dynamically expand the representation according to the complexity of novel concepts by introducing a channel-level mask-based pruning strategy. Moreover, we introduce an auxiliary loss to encourage the model to learn diverse and discriminate features for novel concepts. We conduct extensive experiments on the three class incremental learning benchmarks and our method consistently outperforms other methods with a large margin.

Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human representations. Convexity of object regions in conceptual spaces is argued to promote generalizability, few-shot learning, and interpersonal alignment. Based on these insights, we investigate the notion of convexity of concept regions in machine-learned latent spaces. We develop a set of tools for measuring convexity in sampled data and evaluate emergent convexity in layered representations of state-of-the-art deep networks. We show that convexity is robust to basic re-parametrization and, hence, meaningful as a quality of machine-learned latent spaces. We find that approximate convexity is pervasive in neural representations in multiple application domains, including models of images, audio, human activity, text, and medical images. Generally, we observe that fine-tuning increases the convexity of label regions. We find evidence that pretraining convexity of class label regions predicts subsequent fine-tuning performance.

Vision-language models (VLMs) such as CLIP have shown promising performance on a variety of recognition tasks using the standard zero-shot classification procedure -- computing similarity between the query image and the embedded words for each category. By only using the category name, they neglect to make use of the rich context of additional information that language affords. The procedure gives no intermediate understanding of why a category is chosen, and furthermore provides no mechanism for adjusting the criteria used towards this decision. We present an alternative framework for classification with VLMs, which we call classification by description. We ask VLMs to check for descriptive features rather than broad categories: to find a tiger, look for its stripes; its claws; and more. By basing decisions on these descriptors, we can provide additional cues that encourage using the features we want to be used. In the process, we can get a clear idea of what features the model uses to construct its decision; it gains some level of inherent explainability. We query large language models (e.g., GPT-3) for these descriptors to obtain them in a scalable way. Extensive experiments show our framework has numerous advantages past interpretability. We show improvements in accuracy on ImageNet across distribution shifts; demonstrate the ability to adapt VLMs to recognize concepts unseen during training; and illustrate how descriptors can be edited to effectively mitigate bias compared to the baseline.

Data is a crucial component of machine learning. The field is reliant on data to train, validate, and test models. With increased technical capabilities, machine learning research has boomed in both academic and industry settings, and one major focus has been on computer vision. Computer vision is a popular domain of machine learning increasingly pertinent to real-world applications, from facial recognition in policing to object detection for autonomous vehicles. Given computer vision's propensity to shape machine learning research and impact human life, we seek to understand disciplinary practices around dataset documentation - how data is collected, curated, annotated, and packaged into datasets for computer vision researchers and practitioners to use for model tuning and development. Specifically, we examine what dataset documentation communicates about the underlying values of vision data and the larger practices and goals of computer vision as a field. To conduct this study, we collected a corpus of about 500 computer vision datasets, from which we sampled 114 dataset publications across different vision tasks. Through both a structured and thematic content analysis, we document a number of values around accepted data practices, what makes desirable data, and the treatment of humans in the dataset construction process. We discuss how computer vision datasets authors value efficiency at the expense of care; universality at the expense of contextuality; impartiality at the expense of positionality; and model work at the expense of data work. Many of the silenced values we identify sit in opposition with social computing practices. We conclude with suggestions on how to better incorporate silenced values into the dataset creation and curation process.

Machine learning has been highly successful in data-intensive applications but is often hampered when the data set is small. Recently, Few-Shot Learning (FSL) is proposed to tackle this problem. Using prior knowledge, FSL can rapidly generalize to new tasks containing only a few samples with supervised information. In this paper, we conduct a thorough survey to fully understand FSL. Starting from a formal definition of FSL, we distinguish FSL from several relevant machine learning problems. We then point out that the core issue in FSL is that the empirical risk minimized is unreliable. Based on how prior knowledge can be used to handle this core issue, we categorize FSL methods from three perspectives: (i) data, which uses prior knowledge to augment the supervised experience; (ii) model, which uses prior knowledge to reduce the size of the hypothesis space; and (iii) algorithm, which uses prior knowledge to alter the search for the best hypothesis in the given hypothesis space. With this taxonomy, we review and discuss the pros and cons of each category. Promising directions, in the aspects of the FSL problem setups, techniques, applications and theories, are also proposed to provide insights for future research.

Recent works have shown that, when trained at scale, uni-modal 2D vision and text encoders converge to learned features that share remarkable structural properties, despite arising from different representations. However, the role of 3D encoders with respect to other modalities remains unexplored. Furthermore, existing 3D foundation models that leverage large datasets are typically trained with explicit alignment objectives with respect to frozen encoders from other representations. In this work, we investigate the possibility of a posteriori alignment of representations obtained from uni-modal 3D encoders compared to text-based feature spaces. We show that naive post-training feature alignment of uni-modal text and 3D encoders results in limited performance. We then focus on extracting subspaces of the corresponding feature spaces and discover that by projecting learned representations onto well-chosen lower-dimensional subspaces the quality of alignment becomes significantly higher, leading to improved accuracy on matching and retrieval tasks. Our analysis further sheds light on the nature of these shared subspaces, which roughly separate between semantic and geometric data representations. Overall, ours is the first work that helps to establish a baseline for post-training alignment of 3D uni-modal and text feature spaces, and helps to highlight both the shared and unique properties of 3D data compared to other representations.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Class-agnostic counting (CAC) aims to estimate the number of objects in images without being restricted to predefined categories. However, while current exemplar-based CAC methods offer flexibility at inference time, they still rely heavily on labeled data for training, which limits scalability and generalization to many downstream use cases. In this paper, we introduce CountingDINO, the first training-free exemplar-based CAC framework that exploits a fully unsupervised feature extractor. Specifically, our approach employs self-supervised vision-only backbones to extract object-aware features, and it eliminates the need for annotated data throughout the entire proposed pipeline. At inference time, we extract latent object prototypes via ROI-Align from DINO features and use them as convolutional kernels to generate similarity maps. These are then transformed into density maps through a simple yet effective normalization scheme. We evaluate our approach on the FSC-147 benchmark, where we consistently outperform a baseline based on an SOTA unsupervised object detector under the same label- and training-free setting. Additionally, we achieve competitive results -- and in some cases surpass -- training-free methods that rely on supervised backbones, non-training-free unsupervised methods, as well as several fully supervised SOTA approaches. This demonstrates that label- and training-free CAC can be both scalable and effective. Code: https://lorebianchi98.github.io/CountingDINO/.

Graph neural networks (GNNs) have gained significant attention in recent years for their ability to process data that may be represented as graphs. This has prompted several studies to explore their representational capability based on the graph isomorphism task. Notably, these works inherently assume a countable node feature representation, potentially limiting their applicability. Interestingly, only a few study GNNs with uncountable node feature representation. In the paper, a new perspective on the representational capability of GNNs is investigated across all levelsx2014node-level, neighborhood-level, and graph-levelx2014when the space of node feature representation is uncountable. Specifically, the injective and metric requirements of previous works are softly relaxed by employing a pseudometric distance on the space of input to create a soft-injective function such that distinct inputs may produce similar outputs if and only if the pseudometric deems the inputs to be sufficiently similar on some representation. As a consequence, a simple and computationally efficient soft-isomorphic relational graph convolution network (SIR-GCN) that emphasizes the contextualized transformation of neighborhood feature representations via anisotropic and dynamic message functions is proposed. Furthermore, a mathematical discussion on the relationship between SIR-GCN and key GNNs in literature is laid out to put the contribution into context, establishing SIR-GCN as a generalization of classical GNN methodologies. To close, experiments on synthetic and benchmark datasets demonstrate the relative superiority of SIR-GCN, outperforming comparable models in node and graph property prediction tasks.

Despite the unprecedented success of text-to-image diffusion models, controlling the number of depicted objects using text is surprisingly hard. This is important for various applications from technical documents, to children's books to illustrating cooking recipes. Generating object-correct counts is fundamentally challenging because the generative model needs to keep a sense of separate identity for every instance of the object, even if several objects look identical or overlap, and then carry out a global computation implicitly during generation. It is still unknown if such representations exist. To address count-correct generation, we first identify features within the diffusion model that can carry the object identity information. We then use them to separate and count instances of objects during the denoising process and detect over-generation and under-generation. We fix the latter by training a model that predicts both the shape and location of a missing object, based on the layout of existing ones, and show how it can be used to guide denoising with correct object count. Our approach, CountGen, does not depend on external source to determine object layout, but rather uses the prior from the diffusion model itself, creating prompt-dependent and seed-dependent layouts. Evaluated on two benchmark datasets, we find that CountGen strongly outperforms the count-accuracy of existing baselines.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings. Our code is available at https://github.com/aktsonthalia/rankable-vision-embeddings.

Supervised Fine-Tuning (SFT) serves as a crucial phase in aligning Large Language Models (LLMs) to specific task prerequisites. The selection of fine-tuning data profoundly influences the model's performance, whose principle is traditionally grounded in data quality and distribution. In this paper, we introduce a new dimension in SFT data selection: learnability. This new dimension is motivated by the intuition that SFT unlocks capabilities acquired by a LLM during the pretraining phase. Given that different pretrained models have disparate capabilities, the SFT data appropriate for one may not suit another. Thus, we introduce the term learnability to define the suitability of data for effective learning by the model. We present the Loss Based SFT Data Selection (LoBaSS) method, utilizing data learnability as the principal criterion for the selection SFT data. This method provides a nuanced approach, allowing the alignment of data selection with inherent model capabilities, ensuring optimal compatibility and learning efficiency. In experimental comparisons involving 7B and 13B models, our LoBaSS method is able to surpass full-data fine-tuning at merely 6% of the total training data. When employing 16.7% of the data, LoBaSS harmonizes the model's capabilities across conversational and mathematical domains, proving its efficacy and adaptability.

Several studies have explored the mechanisms of large language models (LLMs) in coding tasks, but most have focused on programming languages (PLs) in a monolingual setting. In this paper, we investigate the relationship between multiple PLs and English in the concept space of LLMs. We perform a few-shot translation task on 21 PL pairs using two Llama-based models. By decoding the embeddings of intermediate layers during this task, we observe that the concept space is closer to English (including PL keywords) and assigns high probabilities to English tokens in the second half of the intermediate layers. We analyze neuron activations for 11 PLs and English, finding that while language-specific neurons are primarily concentrated in the bottom layers, those exclusive to each PL tend to appear in the top layers. For PLs that are highly aligned with multiple other PLs, identifying language-specific neurons is not feasible. These PLs also tend to have a larger keyword set than other PLs and are closer to the model's concept space regardless of the input/output PL in the translation task. Our findings provide insights into how LLMs internally represent PLs, revealing structural patterns in the model's concept space. Code is available at https://github.com/cisnlp/code-specific-neurons.

We propose YOLO-Count, a differentiable open-vocabulary object counting model that tackles both general counting challenges and enables precise quantity control for text-to-image (T2I) generation. A core contribution is the 'cardinality' map, a novel regression target that accounts for variations in object size and spatial distribution. Leveraging representation alignment and a hybrid strong-weak supervision scheme, YOLO-Count bridges the gap between open-vocabulary counting and T2I generation control. Its fully differentiable architecture facilitates gradient-based optimization, enabling accurate object count estimation and fine-grained guidance for generative models. Extensive experiments demonstrate that YOLO-Count achieves state-of-the-art counting accuracy while providing robust and effective quantity control for T2I systems.

This work introduces composed image retrieval to remote sensing. It allows to query a large image archive by image examples alternated by a textual description, enriching the descriptive power over unimodal queries, either visual or textual. Various attributes can be modified by the textual part, such as shape, color, or context. A novel method fusing image-to-image and text-to-image similarity is introduced. We demonstrate that a vision-language model possesses sufficient descriptive power and no further learning step or training data are necessary. We present a new evaluation benchmark focused on color, context, density, existence, quantity, and shape modifications. Our work not only sets the state-of-the-art for this task, but also serves as a foundational step in addressing a gap in the field of remote sensing image retrieval. Code at: https://github.com/billpsomas/rscir

Multimodal Large Language Models (MLLMs) demonstrate remarkable fluency in understanding visual scenes, yet they exhibit a critical lack in a fundamental cognitive skill: object counting. This blind spot severely limits their reliability in real-world applications. To date, this capability has been largely unevaluated in complex scenarios, as existing benchmarks either feature sparse object densities or are confined to specific visual domains, failing to test models under realistic conditions. Addressing this gap, we introduce CountQA, a challenging new benchmark designed to probe this deficiency. Comprising over 1,500 question-answer pairs, CountQA features real-world images with high object density, clutter, and occlusion. We investigate this weakness by evaluating 15 prominent MLLMs on the CountQA benchmark and reveal that the top-performing model achieves a mere 42.9% accuracy, with performance declining as object counts rise. By providing a dedicated benchmark to diagnose and rectify this core weakness, CountQA paves the way for a new generation of MLLMs that are not only descriptively fluent but also numerically grounded and spatially aware. We will open-source the dataset and code upon paper acceptance to foster further research.

We present SliderSpace, a framework for automatically decomposing the visual capabilities of diffusion models into controllable and human-understandable directions. Unlike existing control methods that require a user to specify attributes for each edit direction individually, SliderSpace discovers multiple interpretable and diverse directions simultaneously from a single text prompt. Each direction is trained as a low-rank adaptor, enabling compositional control and the discovery of surprising possibilities in the model's latent space. Through extensive experiments on state-of-the-art diffusion models, we demonstrate SliderSpace's effectiveness across three applications: concept decomposition, artistic style exploration, and diversity enhancement. Our quantitative evaluation shows that SliderSpace-discovered directions decompose the visual structure of model's knowledge effectively, offering insights into the latent capabilities encoded within diffusion models. User studies further validate that our method produces more diverse and useful variations compared to baselines. Our code, data and trained weights are available at https://sliderspace.baulab.info

The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact ell_1 recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Tabular representation learning has recently gained a lot of attention. However, existing approaches only learn a representation from a single table, and thus ignore the potential to learn from the full structure of relational databases, including neighboring tables that can contain important information for a contextualized representation. Moreover, current models are significantly limited in scale, which prevents that they learn from large databases. In this paper, we thus introduce our vision of relational representation learning, that can not only learn from the full relational structure, but also can scale to larger database sizes that are commonly found in real-world. Moreover, we also discuss opportunities and challenges we see along the way to enable this vision and present initial very promising results. Overall, we argue that this direction can lead to foundation models for relational databases that are today only available for text and images.

Large Language Models (LLMs), benefiting from the auto-regressive modelling approach performed on massive unannotated texts corpora, demonstrates powerful perceptual and reasoning capabilities. However, as for extending auto-regressive modelling to multi-modal scenarios to build Large Multi-modal Models (LMMs), there lies a great difficulty that the image information is processed in the LMM as continuous visual embeddings, which cannot obtain discrete supervised labels for classification. In this paper, we successfully perform multi-modal auto-regressive modeling with a unified objective for the first time. Specifically, we propose the concept of visual words, which maps the visual features to probability distributions over LLM's vocabulary, providing supervision information for visual modelling. We further explore the distribution of visual features in the semantic space within LMM and the possibility of using text embeddings to represent visual information. Experimental results and ablation studies on 5 VQA tasks and 4 benchmark toolkits validate the powerful performance of our proposed approach.

We introduce methods for discovering and applying sparse feature circuits. These are causally implicated subnetworks of human-interpretable features for explaining language model behaviors. Circuits identified in prior work consist of polysemantic and difficult-to-interpret units like attention heads or neurons, rendering them unsuitable for many downstream applications. In contrast, sparse feature circuits enable detailed understanding of unanticipated mechanisms. Because they are based on fine-grained units, sparse feature circuits are useful for downstream tasks: We introduce SHIFT, where we improve the generalization of a classifier by ablating features that a human judges to be task-irrelevant. Finally, we demonstrate an entirely unsupervised and scalable interpretability pipeline by discovering thousands of sparse feature circuits for automatically discovered model behaviors.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

The problem of Novel Class Discovery (NCD) consists in extracting knowledge from a labeled set of known classes to accurately partition an unlabeled set of novel classes. While NCD has recently received a lot of attention from the community, it is often solved on computer vision problems and under unrealistic conditions. In particular, the number of novel classes is usually assumed to be known in advance, and their labels are sometimes used to tune hyperparameters. Methods that rely on these assumptions are not applicable in real-world scenarios. In this work, we focus on solving NCD in tabular data when no prior knowledge of the novel classes is available. To this end, we propose to tune the hyperparameters of NCD methods by adapting the k-fold cross-validation process and hiding some of the known classes in each fold. Since we have found that methods with too many hyperparameters are likely to overfit these hidden classes, we define a simple deep NCD model. This method is composed of only the essential elements necessary for the NCD problem and performs impressively well under realistic conditions. Furthermore, we find that the latent space of this method can be used to reliably estimate the number of novel classes. Additionally, we adapt two unsupervised clustering algorithms (k-means and Spectral Clustering) to leverage the knowledge of the known classes. Extensive experiments are conducted on 7 tabular datasets and demonstrate the effectiveness of the proposed method and hyperparameter tuning process, and show that the NCD problem can be solved without relying on knowledge from the novel classes.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Automated feature engineering plays a critical role in improving predictive model performance for tabular learning tasks. Traditional automated feature engineering methods are limited by their reliance on pre-defined transformations within fixed, manually designed search spaces, often neglecting domain knowledge. Recent advances using Large Language Models (LLMs) have enabled the integration of domain knowledge into the feature engineering process. However, existing LLM-based approaches use direct prompting or rely solely on validation scores for feature selection, failing to leverage insights from prior feature discovery experiments or establish meaningful reasoning between feature generation and data-driven performance. To address these challenges, we propose LLM-FE, a novel framework that combines evolutionary search with the domain knowledge and reasoning capabilities of LLMs to automatically discover effective features for tabular learning tasks. LLM-FE formulates feature engineering as a program search problem, where LLMs propose new feature transformation programs iteratively, and data-driven feedback guides the search process. Our results demonstrate that LLM-FE consistently outperforms state-of-the-art baselines, significantly enhancing the performance of tabular prediction models across diverse classification and regression benchmarks.

Given the importance of remote sensing, surprisingly little attention has been paid to it by the representation learning community. To address it and to establish baselines and a common evaluation protocol in this domain, we provide simplified access to 5 diverse remote sensing datasets in a standardized form. Specifically, we investigate in-domain representation learning to develop generic remote sensing representations and explore which characteristics are important for a dataset to be a good source for remote sensing representation learning. The established baselines achieve state-of-the-art performance on these datasets.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

In this paper, we investigate the challenge of integrating tables from data lakes, focusing on three core tasks: 1) pairwise integrability judgment, which determines whether a tuple pair in a table is integrable, accounting for any occurrences of semantic equivalence or typographical errors; 2) integrable set discovery, which aims to identify all integrable sets in a table based on pairwise integrability judgments established in the first task; 3) multi-tuple conflict resolution, which resolves conflicts among multiple tuples during integration. We train a binary classifier to address the task of pairwise integrability judgment. Given the scarcity of labeled data, we propose a self-supervised adversarial contrastive learning algorithm to perform classification, which incorporates data augmentation methods and adversarial examples to autonomously generate new training data. Upon the output of pairwise integrability judgment, each integrable set is considered as a community, a densely connected sub-graph where nodes and edges correspond to tuples in the table and their pairwise integrability, respectively. We proceed to investigate various community detection algorithms to address the integrable set discovery objective. Moving forward to tackle multi-tuple conflict resolution, we introduce an novel in-context learning methodology. This approach capitalizes on the knowledge embedded within pretrained large language models to effectively resolve conflicts that arise when integrating multiple tuples. Notably, our method minimizes the need for annotated data. Since no suitable test collections are available for our tasks, we develop our own benchmarks using two real-word dataset repositories: Real and Join. We conduct extensive experiments on these benchmarks to validate the robustness and applicability of our methodologies in the context of integrating tables within data lakes.

The capabilities of large language models (LLMs) have sparked debate over whether such systems just learn an enormous collection of superficial statistics or a coherent model of the data generating process -- a world model. We find evidence for the latter by analyzing the learned representations of three spatial datasets (world, US, NYC places) and three temporal datasets (historical figures, artworks, news headlines) in the Llama-2 family of models. We discover that LLMs learn linear representations of space and time across multiple scales. These representations are robust to prompting variations and unified across different entity types (e.g. cities and landmarks). In addition, we identify individual ``space neurons'' and ``time neurons'' that reliably encode spatial and temporal coordinates. Our analysis demonstrates that modern LLMs acquire structured knowledge about fundamental dimensions such as space and time, supporting the view that they learn not merely superficial statistics, but literal world models.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

This survey explores the synergistic potential of Large Language Models (LLMs) and Vector Databases (VecDBs), a burgeoning but rapidly evolving research area. With the proliferation of LLMs comes a host of challenges, including hallucinations, outdated knowledge, prohibitive commercial application costs, and memory issues. VecDBs emerge as a compelling solution to these issues by offering an efficient means to store, retrieve, and manage the high-dimensional vector representations intrinsic to LLM operations. Through this nuanced review, we delineate the foundational principles of LLMs and VecDBs and critically analyze their integration's impact on enhancing LLM functionalities. This discourse extends into a discussion on the speculative future developments in this domain, aiming to catalyze further research into optimizing the confluence of LLMs and VecDBs for advanced data handling and knowledge extraction capabilities.

LLMs have revolutionized the field of artificial intelligence and have emerged as the de-facto tool for many tasks. The current established technology of LLMs is to process input and generate output at the token level. This is in sharp contrast to humans who operate at multiple levels of abstraction, well beyond single words, to analyze information and to generate creative content. In this paper, we present an attempt at an architecture which operates on an explicit higher-level semantic representation, which we name a concept. Concepts are language- and modality-agnostic and represent a higher level idea or action in a flow. Hence, we build a "Large Concept Model". In this study, as proof of feasibility, we assume that a concept corresponds to a sentence, and use an existing sentence embedding space, SONAR, which supports up to 200 languages in both text and speech modalities. The Large Concept Model is trained to perform autoregressive sentence prediction in an embedding space. We explore multiple approaches, namely MSE regression, variants of diffusion-based generation, and models operating in a quantized SONAR space. These explorations are performed using 1.6B parameter models and training data in the order of 1.3T tokens. We then scale one architecture to a model size of 7B parameters and training data of about 2.7T tokens. We perform an experimental evaluation on several generative tasks, namely summarization and a new task of summary expansion. Finally, we show that our model exhibits impressive zero-shot generalization performance to many languages, outperforming existing LLMs of the same size. The training code of our models is freely available.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

We study the challenge of achieving theoretically grounded feature recovery using Sparse Autoencoders (SAEs) for the interpretation of Large Language Models. Existing SAE training algorithms often lack rigorous mathematical guarantees and suffer from practical limitations such as hyperparameter sensitivity and instability. To address these issues, we first propose a novel statistical framework for the feature recovery problem, which includes a new notion of feature identifiability by modeling polysemantic features as sparse mixtures of underlying monosemantic concepts. Building on this framework, we introduce a new SAE training algorithm based on ``bias adaptation'', a technique that adaptively adjusts neural network bias parameters to ensure appropriate activation sparsity. We theoretically prove that this algorithm correctly recovers all monosemantic features when input data is sampled from our proposed statistical model. Furthermore, we develop an improved empirical variant, Group Bias Adaptation (GBA), and demonstrate its superior performance against benchmark methods when applied to LLMs with up to 1.5 billion parameters. This work represents a foundational step in demystifying SAE training by providing the first SAE algorithm with theoretical recovery guarantees, thereby advancing the development of more transparent and trustworthy AI systems through enhanced mechanistic interpretability.

Large-scale vision-language models (VLM) have shown impressive results for language-guided search applications. While these models allow category-level queries, they currently struggle with personalized searches for moments in a video where a specific object instance such as ``My dog Biscuit'' appears. We present the following three contributions to address this problem. First, we describe a method to meta-personalize a pre-trained VLM, i.e., learning how to learn to personalize a VLM at test time to search in video. Our method extends the VLM's token vocabulary by learning novel word embeddings specific to each instance. To capture only instance-specific features, we represent each instance embedding as a combination of shared and learned global category features. Second, we propose to learn such personalization without explicit human supervision. Our approach automatically identifies moments of named visual instances in video using transcripts and vision-language similarity in the VLM's embedding space. Finally, we introduce This-Is-My, a personal video instance retrieval benchmark. We evaluate our approach on This-Is-My and DeepFashion2 and show that we obtain a 15% relative improvement over the state of the art on the latter dataset.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

With the introduction of transformer-based models for vision and language tasks, such as LLaVA and Chameleon, there has been renewed interest in the discrete tokenized representation of images. These models often treat image patches as discrete tokens, analogous to words in natural language, learning joint alignments between visual and human languages. However, little is known about the statistical behavior of these visual languages - whether they follow similar frequency distributions, grammatical structures, or topologies as natural languages. In this paper, we take a natural-language-centric approach to analyzing discrete visual languages and uncover striking similarities and fundamental differences. We demonstrate that, although visual languages adhere to Zipfian distributions, higher token innovation drives greater entropy and lower compression, with tokens predominantly representing object parts, indicating intermediate granularity. We also show that visual languages lack cohesive grammatical structures, leading to higher perplexity and weaker hierarchical organization compared to natural languages. Finally, we demonstrate that, while vision models align more closely with natural languages than other models, this alignment remains significantly weaker than the cohesion found within natural languages. Through these experiments, we demonstrate how understanding the statistical properties of discrete visual languages can inform the design of more effective computer vision models.

Example synthesis is one of the leading methods to tackle the problem of few-shot learning, where only a small number of samples per class are available. However, current synthesis approaches only address the scenario of a single category label per image. In this work, we propose a novel technique for synthesizing samples with multiple labels for the (yet unhandled) multi-label few-shot classification scenario. We propose to combine pairs of given examples in feature space, so that the resulting synthesized feature vectors will correspond to examples whose label sets are obtained through certain set operations on the label sets of the corresponding input pairs. Thus, our method is capable of producing a sample containing the intersection, union or set-difference of labels present in two input samples. As we show, these set operations generalize to labels unseen during training. This enables performing augmentation on examples of novel categories, thus, facilitating multi-label few-shot classifier learning. We conduct numerous experiments showing promising results for the label-set manipulation capabilities of the proposed approach, both directly (using the classification and retrieval metrics), and in the context of performing data augmentation for multi-label few-shot learning. We propose a benchmark for this new and challenging task and show that our method compares favorably to all the common baselines.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Survey data can contain a high number of features while having a comparatively low quantity of examples. Machine learning models that attempt to predict outcomes from survey data under these conditions can overfit and result in poor generalizability. One remedy to this issue is feature selection, which attempts to select an optimal subset of features to learn upon. A relatively unexplored source of information in the feature selection process is the usage of textual names of features, which may be semantically indicative of which features are relevant to a target outcome. The relationships between feature names and target names can be evaluated using language models (LMs) to produce semantic textual similarity (STS) scores, which can then be used to select features. We examine the performance using STS to select features directly and in the minimal-redundancy-maximal-relevance (mRMR) algorithm. The performance of STS as a feature selection metric is evaluated against preliminary survey data collected as a part of a clinical study on persistent post-surgical pain (PPSP). The results suggest that features selected with STS can result in higher performance models compared to traditional feature selection algorithms.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Recently, dense contrastive learning has shown superior performance on dense prediction tasks compared to instance-level contrastive learning. Despite its supremacy, the properties of dense contrastive representations have not yet been carefully studied. Therefore, we analyze the theoretical ideas of dense contrastive learning using a standard CNN and straightforward feature matching scheme rather than propose a new complex method. Inspired by the analysis of the properties of instance-level contrastive representations through the lens of alignment and uniformity on the hypersphere, we employ and extend the same lens for the dense contrastive representations to analyze their underexplored properties. We discover the core principle in constructing a positive pair of dense features and empirically proved its validity. Also, we introduces a new scalar metric that summarizes the correlation between alignment-and-uniformity and downstream performance. Using this metric, we study various facets of densely learned contrastive representations such as how the correlation changes over single- and multi-object datasets or linear evaluation and dense prediction tasks. The source code is publicly available at: https://github.com/SuperSupermoon/DenseCL-analysis

We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model slices of music from a large corpus spanning eight musical genres. In this newly learned vector space, a metric based on cosine distance is able to distinguish between functional chord relationships, as well as harmonic associations in the music. Evidence, based on cosine distance between chord-pair vectors, suggests that an implicit circle-of-fifths exists in the vector space. In addition, a comparison between pieces in different keys reveals that key relationships are represented in word2vec space. These results suggest that the newly learned embedded vector representation does in fact capture tonal and harmonic characteristics of music, without receiving explicit information about the musical content of the constituent slices. In order to investigate whether proximity in the discovered space of embeddings is indicative of `semantically-related' slices, we explore a music generation task, by automatically replacing existing slices from a given piece of music with new slices. We propose an algorithm to find substitute slices based on spatial proximity and the pitch class distribution inferred in the chosen subspace. The results indicate that the size of the subspace used has a significant effect on whether slices belonging to the same key are selected. In sum, the proposed word2vec model is able to learn music-vector embeddings that capture meaningful tonal and harmonic relationships in music, thereby providing a useful tool for exploring musical properties and comparisons across pieces, as a potential input representation for deep learning models, and as a music generation device.

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

Object counting has progressed from class-specific models, which count only known categories, to class-agnostic models that generalize to unseen categories. The next challenge is Referring Expression Counting (REC), where the goal is to count objects based on fine-grained attributes and contextual differences. Existing methods struggle with distinguishing visually similar objects that belong to the same category but correspond to different referring expressions. To address this, we propose C-REX, a novel contrastive learning framework, based on supervised contrastive learning, designed to enhance discriminative representation learning. Unlike prior works, C-REX operates entirely within the image space, avoiding the misalignment issues of image-text contrastive learning, thus providing a more stable contrastive signal. It also guarantees a significantly larger pool of negative samples, leading to improved robustness in the learned representations. Moreover, we showcase that our framework is versatile and generic enough to be applied to other similar tasks like class-agnostic counting. To support our approach, we analyze the key components of sota detection-based models and identify that detecting object centroids instead of bounding boxes is the key common factor behind their success in counting tasks. We use this insight to design a simple yet effective detection-based baseline to build upon. Our experiments show that C-REX achieves state-of-the-art results in REC, outperforming previous methods by more than 22\% in MAE and more than 10\% in RMSE, while also demonstrating strong performance in class-agnostic counting. Code is available at https://github.com/cvlab-stonybrook/c-rex.

Contrastive learning (CL) has emerged as a powerful technique for representation learning, with or without label supervision. However, supervised CL is prone to collapsing representations of subclasses within a class by not capturing all their features, and unsupervised CL may suppress harder class-relevant features by focusing on learning easy class-irrelevant features; both significantly compromise representation quality. Yet, there is no theoretical understanding of class collapse or feature suppression at test time. We provide the first unified theoretically rigorous framework to determine which features are learnt by CL. Our analysis indicate that, perhaps surprisingly, bias of (stochastic) gradient descent towards finding simpler solutions is a key factor in collapsing subclass representations and suppressing harder class-relevant features. Moreover, we present increasing embedding dimensionality and improving the quality of data augmentations as two theoretically motivated solutions to {feature suppression}. We also provide the first theoretical explanation for why employing supervised and unsupervised CL together yields higher-quality representations, even when using commonly-used stochastic gradient methods.

Vector space word representations are learned from distributional information of words in large corpora. Although such statistics are semantically informative, they disregard the valuable information that is contained in semantic lexicons such as WordNet, FrameNet, and the Paraphrase Database. This paper proposes a method for refining vector space representations using relational information from semantic lexicons by encouraging linked words to have similar vector representations, and it makes no assumptions about how the input vectors were constructed. Evaluated on a battery of standard lexical semantic evaluation tasks in several languages, we obtain substantial improvements starting with a variety of word vector models. Our refinement method outperforms prior techniques for incorporating semantic lexicons into the word vector training algorithms.

Sequence modeling plays a vital role across various domains, with recurrent neural networks being historically the predominant method of performing these tasks. However, the emergence of transformers has altered this paradigm due to their superior performance. Built upon these advances, transformers have conjoined CNNs as two leading foundational models for learning visual representations. However, transformers are hindered by the O(N^2) complexity of their attention mechanisms, while CNNs lack global receptive fields and dynamic weight allocation. State Space Models (SSMs), specifically the \textbf{Mamba} model with selection mechanisms and hardware-aware architecture, have garnered immense interest lately in sequential modeling and visual representation learning, challenging the dominance of transformers by providing infinite context lengths and offering substantial efficiency maintaining linear complexity in the input sequence. Capitalizing on the advances in computer vision, medical imaging has heralded a new epoch with Mamba models. Intending to help researchers navigate the surge, this survey seeks to offer an encyclopedic review of Mamba models in medical imaging. Specifically, we start with a comprehensive theoretical review forming the basis of SSMs, including Mamba architecture and its alternatives for sequence modeling paradigms in this context. Next, we offer a structured classification of Mamba models in the medical field and introduce a diverse categorization scheme based on their application, imaging modalities, and targeted organs. Finally, we summarize key challenges, discuss different future research directions of the SSMs in the medical domain, and propose several directions to fulfill the demands of this field. In addition, we have compiled the studies discussed in this paper along with their open-source implementations on our GitHub repository.

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. With the interaction tensor, we make several key observations about how features are distributed in data and how models with different random seeds learn different features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form. We demonstrate that the proposed framework can explain empirically observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only unlabeled data. Further, our theory also provides explicit construction of natural data distributions that break the GDE. Thus, we believe this work provides valuable new insight into our understanding of feature learning.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Lung cancer is responsible for 21% of cancer deaths in the UK and five-year survival rates are heavily influenced by the stage the cancer was identified at. Recent studies have demonstrated the capability of AI methods for accurate and early diagnosis of lung cancer from routine scans. However, this evidence has not translated into clinical practice with one barrier being a lack of interpretable models. This study investigates the application Variational Autoencoders (VAEs), a type of generative AI model, to lung cancer lesions. Proposed models were trained on lesions extracted from 3D CT scans in the LIDC-IDRI public dataset. Latent vector representations of 2D slices produced by the VAEs were explored through clustering to justify their quality and used in an MLP classifier model for lung cancer diagnosis, the best model achieved state-of-the-art metrics of AUC 0.98 and 93.1% accuracy. Cluster analysis shows the VAE latent space separates the dataset of malignant and benign lesions based on meaningful feature components including tumour size, shape, patient and malignancy class. We also include a comparative analysis of the standard Gaussian VAE (GVAE) and the more recent Dirichlet VAE (DirVAE), which replaces the prior with a Dirichlet distribution to encourage a more explainable latent space with disentangled feature representation. Finally, we demonstrate the potential for latent space traversals corresponding to clinically meaningful feature changes.

Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as their size or depth. We are not aware of such research for tree ensembles and aim to contribute to this area. Mainly, we provide two novel algorithms and corresponding lower bounds. First, we are able to carry over and substantially improve on tractability results for decision trees, obtaining a (6delta D S)^S cdot poly-time algorithm, where S is the number of cuts in the tree ensemble, D the largest domain size, and delta is the largest number of features in which two examples differ. To achieve this, we introduce the witness-tree technique which also seems promising for practice. Second, we show that dynamic programming, which has been successful for decision trees, may also be viable for tree ensembles, providing an ell^n cdot poly-time algorithm, where ell is the number of trees and n the number of examples. Finally, we compare the number of cuts necessary to classify training data sets for decision trees and tree ensembles, showing that ensembles may need exponentially fewer cuts for increasing number of trees.

Semi-Supervised Semantic Segmentation (S4) aims to train a segmentation model with limited labeled images and a substantial volume of unlabeled images. To improve the robustness of representations, powerful methods introduce a pixel-wise contrastive learning approach in latent space (i.e., representation space) that aggregates the representations to their prototypes in a fully supervised manner. However, previous contrastive-based S4 methods merely rely on the supervision from the model's output (logits) in logit space during unlabeled training. In contrast, we utilize the outputs in both logit space and representation space to obtain supervision in a collaborative way. The supervision from two spaces plays two roles: 1) reduces the risk of over-fitting to incorrect semantic information in logits with the help of representations; 2) enhances the knowledge exchange between the two spaces. Furthermore, unlike previous approaches, we use the similarity between representations and prototypes as a new indicator to tilt training those under-performing representations and achieve a more efficient contrastive learning process. Results on two public benchmarks demonstrate the competitive performance of our method compared with state-of-the-art methods.

Integer sequences are of central importance to the modeling of concepts admitting complete finitary descriptions. We introduce a novel view on the learning of such concepts and lay down a set of benchmarking tasks aimed at conceptual understanding by machine learning models. These tasks indirectly assess model ability to abstract, and challenge them to reason both interpolatively and extrapolatively from the knowledge gained by observing representative examples. To further aid research in knowledge representation and reasoning, we present FACT, the Finitary Abstraction Comprehension Toolkit. The toolkit surrounds a large dataset of integer sequences comprising both organic and synthetic entries, a library for data pre-processing and generation, a set of model performance evaluation tools, and a collection of baseline model implementations, enabling the making of the future advancements with ease.

This paper demonstrates how to use generative models trained for image synthesis as tools for visual data mining. Our insight is that since contemporary generative models learn an accurate representation of their training data, we can use them to summarize the data by mining for visual patterns. Concretely, we show that after finetuning conditional diffusion models to synthesize images from a specific dataset, we can use these models to define a typicality measure on that dataset. This measure assesses how typical visual elements are for different data labels, such as geographic location, time stamps, semantic labels, or even the presence of a disease. This analysis-by-synthesis approach to data mining has two key advantages. First, it scales much better than traditional correspondence-based approaches since it does not require explicitly comparing all pairs of visual elements. Second, while most previous works on visual data mining focus on a single dataset, our approach works on diverse datasets in terms of content and scale, including a historical car dataset, a historical face dataset, a large worldwide street-view dataset, and an even larger scene dataset. Furthermore, our approach allows for translating visual elements across class labels and analyzing consistent changes.

This paper embarks on an exploration into the Large Language Model (LLM) datasets, which play a crucial role in the remarkable advancements of LLMs. The datasets serve as the foundational infrastructure analogous to a root system that sustains and nurtures the development of LLMs. Consequently, examination of these datasets emerges as a critical topic in research. In order to address the current lack of a comprehensive overview and thorough analysis of LLM datasets, and to gain insights into their current status and future trends, this survey consolidates and categorizes the fundamental aspects of LLM datasets from five perspectives: (1) Pre-training Corpora; (2) Instruction Fine-tuning Datasets; (3) Preference Datasets; (4) Evaluation Datasets; (5) Traditional Natural Language Processing (NLP) Datasets. The survey sheds light on the prevailing challenges and points out potential avenues for future investigation. Additionally, a comprehensive review of the existing available dataset resources is also provided, including statistics from 444 datasets, covering 8 language categories and spanning 32 domains. Information from 20 dimensions is incorporated into the dataset statistics. The total data size surveyed surpasses 774.5 TB for pre-training corpora and 700M instances for other datasets. We aim to present the entire landscape of LLM text datasets, serving as a comprehensive reference for researchers in this field and contributing to future studies. Related resources are available at: https://github.com/lmmlzn/Awesome-LLMs-Datasets.

Diffusion models have shown remarkable progress in photorealistic image synthesis, yet they remain unreliable for generating scenes with a precise number of object instances, particularly in complex and high-density settings. We present CountLoop, a training-free framework that provides diffusion models with accurate instance control through iterative structured feedback. The approach alternates between image generation and multimodal agent evaluation, where a language-guided planner and critic assess object counts, spatial arrangements, and attribute consistency. This feedback is then used to refine layouts and guide subsequent generations. To further improve separation between objects, especially in occluded scenes, we introduce instance-driven attention masking and compositional generation techniques. Experiments on COCO Count, T2I CompBench, and two new high-instance benchmarks show that CountLoop achieves counting accuracy of up to 98% while maintaining spatial fidelity and visual quality, outperforming layout-based and gradient-guided baselines with a score of 0.97.

Few Shot Class Incremental Learning (FSCIL) with few examples per class for each incremental session is the realistic setting of continual learning since obtaining large number of annotated samples is not feasible and cost effective. We present the framework MASIL as a step towards learning the maximal separable classifier. It addresses the common problem i.e forgetting of old classes and over-fitting to novel classes by learning the classifier weights to be maximally separable between classes forming a simplex Equiangular Tight Frame. We propose the idea of concept factorization explaining the collapsed features for base session classes in terms of concept basis and use these to induce classifier simplex for few shot classes. We further adds fine tuning to reduce any error occurred during factorization and train the classifier jointly on base and novel classes without retaining any base class samples in memory. Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that MASIL outperforms all the benchmarks.

Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry's under-counting probability can be provably recovered from partial observations -- under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Despite the groundbreaking success of diffusion models in generating high-fidelity images, their latent space remains relatively under-explored, even though it holds significant promise for enabling versatile and interpretable image editing capabilities. The complicated denoising trajectory and high dimensionality of the latent space make it extremely challenging to interpret. Existing methods mainly explore the feature space of U-Net in Diffusion Models (DMs) instead of the latent space itself. In contrast, we directly investigate the latent space via Singular Value Decomposition (SVD) and discover three useful properties that can be used to control generation results without the requirements of data collection and maintain identity fidelity generated images. Based on these properties, we propose a novel image editing framework that is capable of learning arbitrary attributes from one pair of latent codes destined by text prompts in Stable Diffusion Models. To validate our approach, extensive experiments are conducted to demonstrate its effectiveness and flexibility in image editing. We will release our codes soon to foster further research and applications in this area.

Recently the state space models (SSMs) with efficient hardware-aware designs, i.e., Mamba, have shown great potential for long sequence modeling. Building efficient and generic vision backbones purely upon SSMs is an appealing direction. However, representing visual data is challenging for SSMs due to the position-sensitivity of visual data and the requirement of global context for visual understanding. In this paper, we show that the reliance of visual representation learning on self-attention is not necessary and propose a new generic vision backbone with bidirectional Mamba blocks (Vim), which marks the image sequences with position embeddings and compresses the visual representation with bidirectional state space models. On ImageNet classification, COCO object detection, and ADE20k semantic segmentation tasks, Vim achieves higher performance compared to well-established vision transformers like DeiT, while also demonstrating significantly improved computation & memory efficiency. For example, Vim is 2.8times faster than DeiT and saves 86.8% GPU memory when performing batch inference to extract features on images with a resolution of 1248times1248. The results demonstrate that Vim is capable of overcoming the computation & memory constraints on performing Transformer-style understanding for high-resolution images and it has great potential to become the next-generation backbone for vision foundation models. Code is available at https://github.com/hustvl/Vim.

In the real world, the frequency of occurrence of objects is naturally skewed forming long-tail class distributions, which results in poor performance on the statistically rare classes. A promising solution is to mine tail-class examples to balance the training dataset. However, mining tail-class examples is a very challenging task. For instance, most of the otherwise successful uncertainty-based mining approaches struggle due to distortion of class probabilities resulting from skewness in data. In this work, we propose an effective, yet simple, approach to overcome these challenges. Our framework enhances the subdued tail-class activations and, thereafter, uses a one-class data-centric approach to effectively identify tail-class examples. We carry out an exhaustive evaluation of our framework on three datasets spanning over two computer vision tasks. Substantial improvements in the minority-class mining and fine-tuned model's performance strongly corroborate the value of our proposed solution.