Daily Papers

Novel-view synthesis of specular objects like shiny metals or glossy paints remains a significant challenge. Not only the glossy appearance but also global illumination effects, including reflections of other objects in the environment, are critical components to faithfully reproduce a scene. In this paper, we present Neural Directional Encoding (NDE), a view-dependent appearance encoding of neural radiance fields (NeRF) for rendering specular objects. NDE transfers the concept of feature-grid-based spatial encoding to the angular domain, significantly improving the ability to model high-frequency angular signals. In contrast to previous methods that use encoding functions with only angular input, we additionally cone-trace spatial features to obtain a spatially varying directional encoding, which addresses the challenging interreflection effects. Extensive experiments on both synthetic and real datasets show that a NeRF model with NDE (1) outperforms the state of the art on view synthesis of specular objects, and (2) works with small networks to allow fast (real-time) inference. The project webpage and source code are available at: https://lwwu2.github.io/nde/.

Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of indoor environments. Unlike existing methods, which typically assume distant lighting like an environment map, we propose a learnable Gaussian directional encoding to better model the view-dependent effects under near-field lighting conditions. Importantly, our new directional encoding captures the spatially-varying nature of near-field lighting and emulates the behavior of prefiltered environment maps. As a result, it enables the efficient evaluation of preconvolved specular color at any 3D location with varying roughness coefficients. We further introduce a data-driven geometry prior that helps alleviate the shape radiance ambiguity in reflection modeling. We show that our Gaussian directional encoding and geometry prior significantly improve the modeling of challenging specular reflections in neural radiance fields, which helps decompose appearance into more physically meaningful components.

We present Interactive Neural Video Editing (INVE), a real-time video editing solution, which can assist the video editing process by consistently propagating sparse frame edits to the entire video clip. Our method is inspired by the recent work on Layered Neural Atlas (LNA). LNA, however, suffers from two major drawbacks: (1) the method is too slow for interactive editing, and (2) it offers insufficient support for some editing use cases, including direct frame editing and rigid texture tracking. To address these challenges we leverage and adopt highly efficient network architectures, powered by hash-grids encoding, to substantially improve processing speed. In addition, we learn bi-directional functions between image-atlas and introduce vectorized editing, which collectively enables a much greater variety of edits in both the atlas and the frames directly. Compared to LNA, our INVE reduces the learning and inference time by a factor of 5, and supports various video editing operations that LNA cannot. We showcase the superiority of INVE over LNA in interactive video editing through a comprehensive quantitative and qualitative analysis, highlighting its numerous advantages and improved performance. For video results, please see https://gabriel-huang.github.io/inve/

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an O(log n{mu}) upper bound on the time it takes for all neurons to achieve good alignment with the input data, where n is the number of data points and mu measures how well the data are separated. After the early alignment phase, the loss converges to zero at a O(1{t}) rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

Humans experience the world through constantly changing visual stimuli, where scenes can shift and move, change in appearance, and vary in distance. The dynamic nature of visual perception is a fundamental aspect of our daily lives, yet the large majority of research on object and scene processing, particularly using fMRI, has focused on static stimuli. While studies of static image perception are attractive due to their computational simplicity, they impose a strong non-naturalistic constraint on our investigation of human vision. In contrast, dynamic visual stimuli offer a more ecologically-valid approach but present new challenges due to the interplay between spatial and temporal information, making it difficult to disentangle the representations of stable image features and motion. To overcome this limitation -- given dynamic inputs, we explicitly decouple the modeling of static image representations and motion representations in the human brain. Three results demonstrate the feasibility of this approach. First, we show that visual motion information as optical flow can be predicted (or decoded) from brain activity as measured by fMRI. Second, we show that this predicted motion can be used to realistically animate static images using a motion-conditioned video diffusion model (where the motion is driven by fMRI brain activity). Third, we show prediction in the reverse direction: existing video encoders can be fine-tuned to predict fMRI brain activity from video imagery, and can do so more effectively than image encoders. This foundational work offers a novel, extensible framework for interpreting how the human brain processes dynamic visual information.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

We present a Transformer architecture for long-context language modeling that combines global attention with two biologically inspired components: chunked local attention and a gated FIFO memory mechanism. This unified attention block allows the model to efficiently handle both short-range and long-range dependencies without increasing attention cost quadratically. The memory module persistently stores past token representations using a gated update mechanism inspired by recurrent networks. Rotary positional encoding is applied per attention head to enable directionally disentangled, scale-invariant positional signals. The architecture is implemented entirely from scratch in PyTorch, with no reliance on high-level libraries, enabling transparent and modular experimentation. Our model offers a lightweight and extensible design for tasks such as dialogue modeling, code completion, and document understanding.

Understanding functional representations within higher visual cortex is a fundamental question in computational neuroscience. While artificial neural networks pretrained on large-scale datasets exhibit striking representational alignment with human neural responses, learning image-computable models of visual cortex relies on individual-level, large-scale fMRI datasets. The necessity for expensive, time-intensive, and often impractical data acquisition limits the generalizability of encoders to new subjects and stimuli. BraInCoRL uses in-context learning to predict voxelwise neural responses from few-shot examples without any additional finetuning for novel subjects and stimuli. We leverage a transformer architecture that can flexibly condition on a variable number of in-context image stimuli, learning an inductive bias over multiple subjects. During training, we explicitly optimize the model for in-context learning. By jointly conditioning on image features and voxel activations, our model learns to directly generate better performing voxelwise models of higher visual cortex. We demonstrate that BraInCoRL consistently outperforms existing voxelwise encoder designs in a low-data regime when evaluated on entirely novel images, while also exhibiting strong test-time scaling behavior. The model also generalizes to an entirely new visual fMRI dataset, which uses different subjects and fMRI data acquisition parameters. Further, BraInCoRL facilitates better interpretability of neural signals in higher visual cortex by attending to semantically relevant stimuli. Finally, we show that our framework enables interpretable mappings from natural language queries to voxel selectivity.

Language models often exhibit undesirable behavior, e.g., generating toxic or gender-biased text. In the case of neural language models, an encoding of the undesirable behavior is often present in the model's representations. Thus, one natural (and common) approach to prevent the model from exhibiting undesirable behavior is to steer the model's representations in a manner that reduces the probability of it generating undesirable text. This paper investigates the formal and empirical properties of steering functions, i.e., transformation of the neural language model's representations that alter its behavior. First, we derive two optimal, in the least-squares sense, affine steering functions under different constraints. Our theory provides justification for existing approaches and offers a novel, improved steering approach. Second, we offer a series of experiments that demonstrate the empirical effectiveness of the methods in mitigating bias and reducing toxic generation.

A major goal of neuroscience is to understand brain computations during visual processing in naturalistic settings. A dominant approach is to use image-computable deep neural networks trained with different task objectives as a basis for linear encoding models. However, in addition to requiring tuning a large number of parameters, the linear encoding approach ignores the structure of the feature maps both in the brain and the models. Recently proposed alternatives have focused on decomposing the linear mapping to spatial and feature components but focus on finding static receptive fields for units that are applicable only in early visual areas. In this work, we employ the attention mechanism used in the transformer architecture to study how retinotopic visual features can be dynamically routed to category-selective areas in high-level visual processing. We show that this computational motif is significantly more powerful than alternative methods in predicting brain activity during natural scene viewing, across different feature basis models and modalities. We also show that this approach is inherently more interpretable, without the need to create importance maps, by interpreting the attention routing signal for different high-level categorical areas. Our approach proposes a mechanistic model of how visual information from retinotopic maps can be routed based on the relevance of the input content to different category-selective regions.

Self-supervised models have revolutionized speech processing, achieving new levels of performance in a wide variety of tasks with limited resources. However, the inner workings of these models are still opaque. In this paper, we aim to analyze the encoded contextual representation of these foundation models based on their inter- and intra-model similarity, independent of any external annotation and task-specific constraint. We examine different SSL models varying their training paradigm -- Contrastive (Wav2Vec2.0) and Predictive models (HuBERT); and model sizes (base and large). We explore these models on different levels of localization/distributivity of information including (i) individual neurons; (ii) layer representation; (iii) attention weights and (iv) compare the representations with their finetuned counterparts.Our results highlight that these models converge to similar representation subspaces but not to similar neuron-localized concepts\footnote{A concept represents a coherent fragment of knowledge, such as ``a class containing certain objects as elements, where the objects have certain properties. We made the code publicly available for facilitating further research, we publicly released our code.

Sentiment is a pervasive feature in natural language text, yet it is an open question how sentiment is represented within Large Language Models (LLMs). In this study, we reveal that across a range of models, sentiment is represented linearly: a single direction in activation space mostly captures the feature across a range of tasks with one extreme for positive and the other for negative. Through causal interventions, we isolate this direction and show it is causally relevant in both toy tasks and real world datasets such as Stanford Sentiment Treebank. Through this case study we model a thorough investigation of what a single direction means on a broad data distribution. We further uncover the mechanisms that involve this direction, highlighting the roles of a small subset of attention heads and neurons. Finally, we discover a phenomenon which we term the summarization motif: sentiment is not solely represented on emotionally charged words, but is additionally summarized at intermediate positions without inherent sentiment, such as punctuation and names. We show that in Stanford Sentiment Treebank zero-shot classification, 76% of above-chance classification accuracy is lost when ablating the sentiment direction, nearly half of which (36%) is due to ablating the summarized sentiment direction exclusively at comma positions.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Hallucinations in large language models are a widespread problem, yet the mechanisms behind whether models will hallucinate are poorly understood, limiting our ability to solve this problem. Using sparse autoencoders as an interpretability tool, we discover that a key part of these mechanisms is entity recognition, where the model detects if an entity is one it can recall facts about. Sparse autoencoders uncover meaningful directions in the representation space, these detect whether the model recognizes an entity, e.g. detecting it doesn't know about an athlete or a movie. This suggests that models can have self-knowledge: internal representations about their own capabilities. These directions are causally relevant: capable of steering the model to refuse to answer questions about known entities, or to hallucinate attributes of unknown entities when it would otherwise refuse. We demonstrate that despite the sparse autoencoders being trained on the base model, these directions have a causal effect on the chat model's refusal behavior, suggesting that chat finetuning has repurposed this existing mechanism. Furthermore, we provide an initial exploration into the mechanistic role of these directions in the model, finding that they disrupt the attention of downstream heads that typically move entity attributes to the final token.

One of the roadblocks to a better understanding of neural networks' internals is polysemanticity, where neurons appear to activate in multiple, semantically distinct contexts. Polysemanticity prevents us from identifying concise, human-understandable explanations for what neural networks are doing internally. One hypothesised cause of polysemanticity is superposition, where neural networks represent more features than they have neurons by assigning features to an overcomplete set of directions in activation space, rather than to individual neurons. Here, we attempt to identify those directions, using sparse autoencoders to reconstruct the internal activations of a language model. These autoencoders learn sets of sparsely activating features that are more interpretable and monosemantic than directions identified by alternative approaches, where interpretability is measured by automated methods. Ablating these features enables precise model editing, for example, by removing capabilities such as pronoun prediction, while disrupting model behaviour less than prior techniques. This work indicates that it is possible to resolve superposition in language models using a scalable, unsupervised method. Our method may serve as a foundation for future mechanistic interpretability work, which we hope will enable greater model transparency and steerability.

Interpretability researchers have attempted to understand MLP neurons of language models based on both the contexts in which they activate and their output weight vectors. They have paid little attention to a complementary aspect: the interactions between input and output. For example, when neurons detect a direction in the input, they might add much the same direction to the residual stream ("enrichment neurons") or reduce its presence ("depletion neurons"). We address this aspect by examining the cosine similarity between input and output weights of a neuron. We apply our method to 12 models and find that enrichment neurons dominate in early-middle layers whereas later layers tend more towards depletion. To explain this finding, we argue that enrichment neurons are largely responsible for enriching concept representations, one of the first steps of factual recall. Our input-output perspective is a complement to activation-dependent analyses and to approaches that treat input and output separately.

We study the intriguing connection between visual data, deep networks, and the brain. Our method creates a universal channel alignment by using brain voxel fMRI response prediction as the training objective. We discover that deep networks, trained with different objectives, share common feature channels across various models. These channels can be clustered into recurring sets, corresponding to distinct brain regions, indicating the formation of visual concepts. Tracing the clusters of channel responses onto the images, we see semantically meaningful object segments emerge, even without any supervised decoder. Furthermore, the universal feature alignment and the clustering of channels produce a picture and quantification of how visual information is processed through the different network layers, which produces precise comparisons between the networks.

The Backpropagation algorithm, widely used to train neural networks, has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, and avoid to back-propagate gradients in favour of using local learning rules, the recently introduced Forward-Forward algorithm replaces the traditional forward and backward passes of Backpropagation with two forward passes. In this work, we show that internal representations obtained with the Forward-Forward algorithm organize into robust, category-specific ensembles, composed by an extremely low number of active units (high sparsity). This is remarkably similar to what is observed in cortical representations during sensory processing. While not found in models trained with standard Backpropagation, sparsity emerges also in networks optimized by Backpropagation, on the same training objective of Forward-Forward. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

Visual search is a ubiquitous and often challenging daily task, exemplified by looking for the car keys at home or a friend in a crowd. An intriguing property of some classical search tasks is an asymmetry such that finding a target A among distractors B can be easier than finding B among A. To elucidate the mechanisms responsible for asymmetry in visual search, we propose a computational model that takes a target and a search image as inputs and produces a sequence of eye movements until the target is found. The model integrates eccentricity-dependent visual recognition with target-dependent top-down cues. We compared the model against human behavior in six paradigmatic search tasks that show asymmetry in humans. Without prior exposure to the stimuli or task-specific training, the model provides a plausible mechanism for search asymmetry. We hypothesized that the polarity of search asymmetry arises from experience with the natural environment. We tested this hypothesis by training the model on augmented versions of ImageNet where the biases of natural images were either removed or reversed. The polarity of search asymmetry disappeared or was altered depending on the training protocol. This study highlights how classical perceptual properties can emerge in neural network models, without the need for task-specific training, but rather as a consequence of the statistical properties of the developmental diet fed to the model. All source code and data are publicly available at https://github.com/kreimanlab/VisualSearchAsymmetry.

The Transformer architecture processes sequences by implementing a form of neural message-passing that consists of iterative information retrieval (attention), followed by local processing (position-wise MLP). Two types of information are essential under this general computational paradigm: "sensory" information about individual objects, and "relational" information describing the relationships between objects. Standard attention naturally encodes the former, but does not explicitly encode the latter. In this paper, we present an extension of Transformers where multi-head attention is augmented with two distinct types of attention heads, each routing information of a different type. The first type is the standard attention mechanism of Transformers, which captures object-level features, while the second type is a novel attention mechanism we propose to explicitly capture relational information. The two types of attention heads each possess different inductive biases, giving the resulting architecture greater efficiency and versatility. The promise of this approach is demonstrated empirically across a range of tasks.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

Classical models of memory in psychology and neuroscience rely on similarity-based retrieval of stored patterns, where similarity is a function of retrieval cues and the stored patterns. While parsimonious, these models do not allow distinct representations for storage and retrieval, despite their distinct computational demands. Key-value memory systems, in contrast, distinguish representations used for storage (values) and those used for retrieval (keys). This allows key-value memory systems to optimize simultaneously for fidelity in storage and discriminability in retrieval. We review the computational foundations of key-value memory, its role in modern machine learning systems, related ideas from psychology and neuroscience, applications to a number of empirical puzzles, and possible biological implementations.

Causal transformer language models (LMs), such as GPT-3, typically require some form of positional encoding, such as positional embeddings. However, we show that LMs without any explicit positional encoding are still competitive with standard models, and that this phenomenon is robust across different datasets, model sizes, and sequence lengths. Probing experiments reveal that such models acquire an implicit notion of absolute positions throughout the network, effectively compensating for the missing information. We conjecture that causal attention enables the model to infer the number of predecessors that each token can attend to, thereby approximating its absolute position. Our findings indicate that causal LMs might derive positional awareness not only from the explicit positioning mechanism, but also from the effects of the causal mask.

Contextual hallucinations -- statements unsupported by given context -- remain a significant challenge in AI. We demonstrate a practical interpretability insight: a generator-agnostic observer model detects hallucinations via a single forward pass and a linear probe on its residual stream. This probe isolates a single, transferable linear direction separating hallucinated from faithful text, outperforming baselines by 5-27 points and showing robust mid-layer performance across Gemma-2 models (2B to 27B). Gradient-times-activation localises this signal to sparse, late-layer MLP activity. Critically, manipulating this direction causally steers generator hallucination rates, proving its actionability. Our results offer novel evidence of internal, low-dimensional hallucination tracking linked to specific MLP sub-circuits, exploitable for detection and mitigation. We release the 2000-example ContraTales benchmark for realistic assessment of such solutions.

We create a reusable Transformer, BrainBERT, for intracranial recordings bringing modern representation learning approaches to neuroscience. Much like in NLP and speech recognition, this Transformer enables classifying complex concepts, i.e., decoding neural data, with higher accuracy and with much less data by being pretrained in an unsupervised manner on a large corpus of unannotated neural recordings. Our approach generalizes to new subjects with electrodes in new positions and to unrelated tasks showing that the representations robustly disentangle the neural signal. Just like in NLP where one can study language by investigating what a language model learns, this approach opens the door to investigating the brain by what a model of the brain learns. As a first step along this path, we demonstrate a new analysis of the intrinsic dimensionality of the computations in different areas of the brain. To construct these representations, we combine a technique for producing super-resolution spectrograms of neural data with an approach designed for generating contextual representations of audio by masking. In the future, far more concepts will be decodable from neural recordings by using representation learning, potentially unlocking the brain like language models unlocked language.

As we show in this paper, the prediction for output token n+1 of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens 1, 2, ..., n-1. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location k in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

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.

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive picture of their inner workings remains a significant challenge. To this end, we set out to understand small transformer models in a more tractable setting: that of solving mazes. In this work, we focus on the abstractions formed by these models and find evidence for the consistent emergence of structured internal representations of maze topology and valid paths. We demonstrate this by showing that the residual stream of only a single token can be linearly decoded to faithfully reconstruct the entire maze. We also find that the learned embeddings of individual tokens have spatial structure. Furthermore, we take steps towards deciphering the circuity of path-following by identifying attention heads (dubbed adjacency heads), which are implicated in finding valid subsequent tokens.

The dominant paradigm for neural text generation is left-to-right decoding from autoregressive language models. Constrained or controllable generation under complex lexical constraints, however, requires foresight to plan ahead feasible future paths. Drawing inspiration from the A* search algorithm, we propose NeuroLogic A*esque, a decoding algorithm that incorporates heuristic estimates of future cost. We develop efficient lookahead heuristics that are efficient for large-scale language models, making our method a drop-in replacement for common techniques such as beam search and top-k sampling. To enable constrained generation, we build on NeuroLogic decoding (Lu et al., 2021), combining its flexibility in incorporating logical constraints with A*esque estimates of future constraint satisfaction. Our approach outperforms competitive baselines on five generation tasks, and achieves new state-of-the-art performance on table-to-text generation, constrained machine translation, and keyword-constrained generation. The improvements are particularly notable on tasks that require complex constraint satisfaction or in few-shot or zero-shot settings. NeuroLogic A*esque illustrates the power of decoding for improving and enabling new capabilities of large-scale language models.

As Large Language Models (LLMs) continue to advance, they exhibit certain cognitive patterns similar to those of humans that are not directly specified in training data. This study investigates this phenomenon by focusing on temporal cognition in LLMs. Leveraging the similarity judgment task, we find that larger models spontaneously establish a subjective temporal reference point and adhere to the Weber-Fechner law, whereby the perceived distance logarithmically compresses as years recede from this reference point. To uncover the mechanisms behind this behavior, we conducted multiple analyses across neuronal, representational, and informational levels. We first identify a set of temporal-preferential neurons and find that this group exhibits minimal activation at the subjective reference point and implements a logarithmic coding scheme convergently found in biological systems. Probing representations of years reveals a hierarchical construction process, where years evolve from basic numerical values in shallow layers to abstract temporal orientation in deep layers. Finally, using pre-trained embedding models, we found that the training corpus itself possesses an inherent, non-linear temporal structure, which provides the raw material for the model's internal construction. In discussion, we propose an experientialist perspective for understanding these findings, where the LLMs' cognition is viewed as a subjective construction of the external world by its internal representational system. This nuanced perspective implies the potential emergence of alien cognitive frameworks that humans cannot intuitively predict, pointing toward a direction for AI alignment that focuses on guiding internal constructions. Our code is available at https://TheOtherMind.github.io.

Recent studies in interpretability have explored the inner workings of transformer models trained on tasks across various domains, often discovering that these networks naturally develop highly structured representations. When such representations comprehensively reflect the task domain's structure, they are commonly referred to as "World Models" (WMs). In this work, we identify WMs in transformers trained on maze-solving tasks. By using Sparse Autoencoders (SAEs) and analyzing attention patterns, we examine the construction of WMs and demonstrate consistency between SAE feature-based and circuit-based analyses. By subsequently intervening on isolated features to confirm their causal role, we find that it is easier to activate features than to suppress them. Furthermore, we find that models can reason about mazes involving more simultaneously active features than they encountered during training; however, when these same mazes (with greater numbers of connections) are provided to models via input tokens instead, the models fail. Finally, we demonstrate that positional encoding schemes appear to influence how World Models are structured within the model's residual stream.

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where L_2 distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

State-of-the-art systems neuroscience experiments yield large-scale multimodal data, and these data sets require new tools for analysis. Inspired by the success of large pretrained models in vision and language domains, we reframe the analysis of large-scale, cellular-resolution neuronal spiking data into an autoregressive spatiotemporal generation problem. Neuroformer is a multimodal, multitask generative pretrained transformer (GPT) model that is specifically designed to handle the intricacies of data in systems neuroscience. It scales linearly with feature size, can process an arbitrary number of modalities, and is adaptable to downstream tasks, such as predicting behavior. We first trained Neuroformer on simulated datasets, and found that it both accurately predicted simulated neuronal circuit activity, and also intrinsically inferred the underlying neural circuit connectivity, including direction. When pretrained to decode neural responses, the model predicted the behavior of a mouse with only few-shot fine-tuning, suggesting that the model begins learning how to do so directly from the neural representations themselves, without any explicit supervision. We used an ablation study to show that joint training on neuronal responses and behavior boosted performance, highlighting the model's ability to associate behavioral and neural representations in an unsupervised manner. These findings show that Neuroformer can analyze neural datasets and their emergent properties, informing the development of models and hypotheses associated with the brain.

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.

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.

Attending to what is relevant is fundamental to both the mammalian brain and modern machine learning models such as Transformers. Yet, determining relevance remains a core challenge, traditionally offloaded to learning algorithms like backpropagation. Inspired by recent cellular neurobiological evidence linking neocortical pyramidal cells to distinct mental states, this work shows how models (e.g., Transformers) can emulate high-level perceptual processing and awake thought (imagination) states to pre-select relevant information before applying attention. Triadic neuronal-level modulation loops among questions (Q), clues (keys, K), and hypotheses (values, V) enable diverse, deep, parallel reasoning chains at the representation level and allow a rapid shift from initial biases to refined understanding. This leads to orders-of-magnitude faster learning with significantly reduced computational demand (e.g., fewer heads, layers, and tokens), at an approximate cost of O(N), where N is the number of input tokens. Results span reinforcement learning (e.g., CarRacing in a high-dimensional visual setup), computer vision, and natural language question answering.

Modeling users' dynamic and evolving preferences from their historical behaviors is challenging and crucial for recommendation systems. Previous methods employ sequential neural networks (e.g., Recurrent Neural Network) to encode users' historical interactions from left to right into hidden representations for making recommendations. Although these methods achieve satisfactory results, they often assume a rigidly ordered sequence which is not always practical. We argue that such left-to-right unidirectional architectures restrict the power of the historical sequence representations. For this purpose, we introduce a Bidirectional Encoder Representations from Transformers for sequential Recommendation (BERT4Rec). However, jointly conditioning on both left and right context in deep bidirectional model would make the training become trivial since each item can indirectly "see the target item". To address this problem, we train the bidirectional model using the Cloze task, predicting the masked items in the sequence by jointly conditioning on their left and right context. Comparing with predicting the next item at each position in a sequence, the Cloze task can produce more samples to train a more powerful bidirectional model. Extensive experiments on four benchmark datasets show that our model outperforms various state-of-the-art sequential models consistently.

Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged. Alternative schemes have been devised; yet, under the constraint of synaptic asymmetry, none have scaled to modern deep learning tasks and architectures. Here, we challenge this perspective, and study the applicability of Direct Feedback Alignment to neural view synthesis, recommender systems, geometric learning, and natural language processing. In contrast with previous studies limited to computer vision tasks, our findings show that it successfully trains a large range of state-of-the-art deep learning architectures, with performance close to fine-tuned backpropagation. At variance with common beliefs, our work supports that challenging tasks can be tackled in the absence of weight transport.

Attention Model has now become an important concept in neural networks that has been researched within diverse application domains. This survey provides a structured and comprehensive overview of the developments in modeling attention. In particular, we propose a taxonomy which groups existing techniques into coherent categories. We review salient neural architectures in which attention has been incorporated, and discuss applications in which modeling attention has shown a significant impact. We also describe how attention has been used to improve the interpretability of neural networks. Finally, we discuss some future research directions in attention. We hope this survey will provide a succinct introduction to attention models and guide practitioners while developing approaches for their applications.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

A fundamental question in cognitive neuroscience is what shapes visual perception: the external world's structure or the brain's internal architecture. Although some perceptual variability can be traced to individual differences, brain responses to naturalistic stimuli evoke similar activity patterns across individuals, suggesting a convergent representational principle. Here, we test if this stimulus-driven convergence follows a common trajectory across people and deep neural networks (DNNs) during its transformation from sensory to high-level internal representations. We introduce a unified framework that traces representational flow by combining inter-subject similarity with alignment to model hierarchies. Applying this framework to three independent fMRI datasets of visual scene perception, we reveal a cortex-wide network, conserved across individuals, organized into two pathways: a medial-ventral stream for scene structure and a lateral-dorsal stream tuned for social and biological content. This functional organization is captured by the hierarchies of vision DNNs but not language models, reinforcing the specificity of the visual-to-semantic transformation. These findings show a convergent computational solution for visual encoding in both human and artificial vision, driven by the structure of the external world.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Transformers with causal attention can solve tasks that require positional information without using positional encodings. In this work, we propose and investigate a new hypothesis about how positional information can be stored without using explicit positional encoding. We observe that nearby embeddings are more similar to each other than faraway embeddings, allowing the transformer to potentially reconstruct the positions of tokens. We show that this pattern can occur in both the trained and the randomly initialized Transformer models with causal attention and no positional encodings over a common range of hyperparameters.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

Despite their remarkable success and deployment across diverse workflows, language models sometimes produce untruthful responses. Our limited understanding of how truthfulness is mechanistically encoded within these models jeopardizes their reliability and safety. In this paper, we propose a method for identifying representations of truthfulness at the neuron level. We show that language models contain truth neurons, which encode truthfulness in a subject-agnostic manner. Experiments conducted across models of varying scales validate the existence of truth neurons, confirming that the encoding of truthfulness at the neuron level is a property shared by many language models. The distribution patterns of truth neurons over layers align with prior findings on the geometry of truthfulness. Selectively suppressing the activations of truth neurons found through the TruthfulQA dataset degrades performance both on TruthfulQA and on other benchmarks, showing that the truthfulness mechanisms are not tied to a specific dataset. Our results offer novel insights into the mechanisms underlying truthfulness in language models and highlight potential directions toward improving their trustworthiness and reliability.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

Can we localize the weights and mechanisms used by a language model to memorize and recite entire paragraphs of its training data? In this paper, we show that while memorization is spread across multiple layers and model components, gradients of memorized paragraphs have a distinguishable spatial pattern, being larger in lower model layers than gradients of non-memorized examples. Moreover, the memorized examples can be unlearned by fine-tuning only the high-gradient weights. We localize a low-layer attention head that appears to be especially involved in paragraph memorization. This head is predominantly focusing its attention on distinctive, rare tokens that are least frequent in a corpus-level unigram distribution. Next, we study how localized memorization is across the tokens in the prefix by perturbing tokens and measuring the caused change in the decoding. A few distinctive tokens early in a prefix can often corrupt the entire continuation. Overall, memorized continuations are not only harder to unlearn, but also to corrupt than non-memorized ones.

A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach -- Brain Diffusion for Visual Exploration ("BrainDiVE") -- builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

Predictor-based methods have substantially enhanced Neural Architecture Search (NAS) optimization. The efficacy of these predictors is largely influenced by the method of encoding neural network architectures. While traditional encodings used an adjacency matrix describing the graph structure of a neural network, novel encodings embrace a variety of approaches from unsupervised pretraining of latent representations to vectors of zero-cost proxies. In this paper, we categorize and investigate neural encodings from three main types: structural, learned, and score-based. Furthermore, we extend these encodings and introduce unified encodings, that extend NAS predictors to multiple search spaces. Our analysis draws from experiments conducted on over 1.5 million neural network architectures on NAS spaces such as NASBench-101 (NB101), NB201, NB301, Network Design Spaces (NDS), and TransNASBench-101. Building on our study, we present our predictor FLAN: Flow Attention for NAS. FLAN integrates critical insights on predictor design, transfer learning, and unified encodings to enable more than an order of magnitude cost reduction for training NAS accuracy predictors. Our implementation and encodings for all neural networks are open-sourced at https://github.com/abdelfattah-lab/flan_nas{https://github.com/abdelfattah-lab/flan\_nas}.

Many papers have shown that attention heads work in conjunction with each other to perform complex tasks. It's frequently assumed that communication between attention heads is via the addition of specific features to token residuals. In this work we seek to isolate and identify the features used to effect communication and coordination among attention heads in GPT-2 small. Our key leverage on the problem is to show that these features are very often sparsely coded in the singular vectors of attention head matrices. We characterize the dimensionality and occurrence of these signals across the attention heads in GPT-2 small when used for the Indirect Object Identification (IOI) task. The sparse encoding of signals, as provided by attention head singular vectors, allows for efficient separation of signals from the residual background and straightforward identification of communication paths between attention heads. We explore the effectiveness of this approach by tracing portions of the circuits used in the IOI task. Our traces reveal considerable detail not present in previous studies, shedding light on the nature of redundant paths present in GPT-2. And our traces go beyond previous work by identifying features used to communicate between attention heads when performing IOI.

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we conduct a direct analysis of the visual information contained in representations by asking the following question: given an encoding of an image, to which extent is it possible to reconstruct the image itself? To answer this question we contribute a general framework to invert representations. We show that this method can invert representations such as HOG and SIFT more accurately than recent alternatives while being applicable to CNNs too. We then use this technique to study the inverse of recent state-of-the-art CNN image representations for the first time. Among our findings, we show that several layers in CNNs retain photographically accurate information about the image, with different degrees of geometric and photometric invariance.

We introduce UniToken, an auto-regressive generation model that encodes visual inputs through a combination of discrete and continuous representations, enabling seamless integration of unified visual understanding and image generation tasks. Unlike previous approaches that rely on unilateral visual representations, our unified visual encoding framework captures both high-level semantics and low-level details, delivering multidimensional information that empowers heterogeneous tasks to selectively assimilate domain-specific knowledge based on their inherent characteristics. Through in-depth experiments, we uncover key principles for developing a unified model capable of both visual understanding and image generation. Extensive evaluations across a diverse range of prominent benchmarks demonstrate that UniToken achieves state-of-the-art performance, surpassing existing approaches. These results establish UniToken as a robust foundation for future research in this domain. The code and models are available at https://github.com/SxJyJay/UniToken.

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that reinterprets the core computation of attention as Pavlovian conditioning. Our model finds a direct mathematical analogue in linear attention, which simplifies the analysis of the underlying associative process. We demonstrate that attention's queries, keys, and values can be mapped to the three elements of classical conditioning: test stimuli that probe associations, conditional stimuli (CS) that serve as retrieval cues, and unconditional stimuli (US) that contain response information. Through this lens, we suggest that each attention operation constructs a transient associative memory via a Hebbian rule, where CS-US pairs form dynamic associations that test stimuli can later retrieve. Our framework yields several theoretical insights grounded in this linearized model: (1) a capacity theorem showing that attention heads can store O(d_k) associations before interference degrades retrieval; (2) an error propagation analysis revealing fundamental architectural trade-offs of balancing model depth, width, and head redundancy to maintain reliability; and (3) an understanding of how biologically plausible learning rules could enhance transformer architectures. By establishing this deep connection, we suggest that the success of modern AI may stem not from architectural novelty alone, but from implementing computational principles that biology optimized over millions of years of evolution.

Human brains respond to semantic features of presented stimuli with different neurons. It is then curious whether modern deep neural networks admit a similar behavior pattern. Specifically, this paper finds a small cluster of neurons in a diffusion model corresponding to a particular subject. We call those neurons the concept neurons. They can be identified by statistics of network gradients to a stimulation connected with the given subject. The concept neurons demonstrate magnetic properties in interpreting and manipulating generation results. Shutting them can directly yield the related subject contextualized in different scenes. Concatenating multiple clusters of concept neurons can vividly generate all related concepts in a single image. A few steps of further fine-tuning can enhance the multi-concept capability, which may be the first to manage to generate up to four different subjects in a single image. For large-scale applications, the concept neurons are environmentally friendly as we only need to store a sparse cluster of int index instead of dense float32 values of the parameters, which reduces storage consumption by 90\% compared with previous subject-driven generation methods. Extensive qualitative and quantitative studies on diverse scenarios show the superiority of our method in interpreting and manipulating diffusion models.

Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Recent work in mechanistic interpretability has shown that behaviors in language models can be successfully reverse-engineered through circuit analysis. A common criticism, however, is that each circuit is task-specific, and thus such analysis cannot contribute to understanding the models at a higher level. In this work, we present evidence that insights (both low-level findings about specific heads and higher-level findings about general algorithms) can indeed generalize across tasks. Specifically, we study the circuit discovered in Wang et al. (2022) for the Indirect Object Identification (IOI) task and 1.) show that it reproduces on a larger GPT2 model, and 2.) that it is mostly reused to solve a seemingly different task: Colored Objects (Ippolito & Callison-Burch, 2023). We provide evidence that the process underlying both tasks is functionally very similar, and contains about a 78% overlap in in-circuit attention heads. We further present a proof-of-concept intervention experiment, in which we adjust four attention heads in middle layers in order to 'repair' the Colored Objects circuit and make it behave like the IOI circuit. In doing so, we boost accuracy from 49.6% to 93.7% on the Colored Objects task and explain most sources of error. The intervention affects downstream attention heads in specific ways predicted by their interactions in the IOI circuit, indicating that this subcircuit behavior is invariant to the different task inputs. Overall, our results provide evidence that it may yet be possible to explain large language models' behavior in terms of a relatively small number of interpretable task-general algorithmic building blocks and computational components.

Large Language Models (LLMs) require high quality preference datasets to align with human preferences. However, conventional methods for constructing such datasets face significant challenges: reliance on pre-collected instructions often leads to distribution mismatches with target models, while the need for sampling multiple stochastic responses introduces substantial computational overhead. In this work, we explore a paradigm shift by leveraging inherent regulation of LLMs' representation space for efficient and tailored preference dataset construction, named Icon^{2}. Specifically, it first extracts layer-wise direction vectors to encode sophisticated human preferences and then uses these vectors to filter self-synthesized instructions based on their inherent consistency. During decoding, bidirectional inherent control is applied to steer token representations, enabling the precise generation of response pairs with clear alignment distinctions. Experimental results demonstrate significant improvements in both alignment and efficiency. Llama3-8B and Qwen2-7B achieve an average win rate improvement of 13.89% on AlpacaEval 2.0 and 13.45% on Arena-Hard, while reducing computational costs by up to 48.1%.

Language models demonstrate remarkable capacity to generalize representations learned in one modality to downstream tasks in other modalities. Can we trace this ability to individual neurons? We study the case where a frozen text transformer is augmented with vision using a self-supervised visual encoder and a single linear projection learned on an image-to-text task. Outputs of the projection layer are not immediately decodable into language describing image content; instead, we find that translation between modalities occurs deeper within the transformer. We introduce a procedure for identifying "multimodal neurons" that convert visual representations into corresponding text, and decoding the concepts they inject into the model's residual stream. In a series of experiments, we show that multimodal neurons operate on specific visual concepts across inputs, and have a systematic causal effect on image captioning.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the appearance of robust associative memories. We first propose a simplified model of noise in the brain, taking into account synaptic noise and interference from neurons external to the network. When coarsely quantized, we show that this noise can be reduced to insertions and erasures. We take a neural network with recurrent modifiable connections, and subject it to noisy external inputs. We introduce an energy usage limitation principle in the network as well as consolidated Hebbian learning, resulting in an incremental processing of inputs. We show that the connections naturally formed correspond to state-of-the-art binary sparse associative memories.

We demonstrate that the inference operations of several open-weight large language models (LLMs) can be mapped to an exactly equivalent linear system for an input sequence without modifying the model weights or altering output predictions. Extending techniques from image diffusion models that exhibit local or piecewise linearity, we strategically alter the gradient computation with respect to a given input sequence for a next-token prediction such that the Jacobian of the model nearly exactly reproduces the forward prediction with a linear system. We demonstrate this approach across models (Llama 3, Gemma 3, Qwen 3, Phi 4, Mistral Ministral and OLMo 2, up to Llama 3.3 70B Q4) and show through the singular value decomposition of the detached Jacobian that these LLMs operate in extremely low-dimensional subspaces where many of the largest singular vectors decode to concepts related to the most-likely output token. This approach also allows us to examine the operation of each successive layer (and its attention and MLP components) as nearly-exact linear systems and observe the emergence of semantic concepts. Despite their expressive power and global nonlinearity, modern LLMs can be interpreted through nearly-exact locally linear decompositions that provide insights into their internal representations and reveal interpretable semantic structures in the next-token prediction process.

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows networks to learn optimal per-neuron activation functions while preserving computational efficiency at inference. In the first phase, neurons adaptively select from a pool of candidate activation functions (ReLU, Sigmoid, Tanh, Leaky ReLU, ELU, SELU) using a differentiable hard-mixture mechanism. In the second phase, each neuron's activation function is fixed according to the learned selection, resulting in a computationally efficient network that supports continued training with optimized vectorized operations. We evaluate SmartMixed on the MNIST dataset using feedforward neural networks of varying depths. The analysis shows that neurons in different layers exhibit distinct preferences for activation functions, providing insights into the functional diversity within neural architectures.

Our environment is filled with rich and dynamic acoustic information. When we walk into a cathedral, the reverberations as much as appearance inform us of the sanctuary's wide open space. Similarly, as an object moves around us, we expect the sound emitted to also exhibit this movement. While recent advances in learned implicit functions have led to increasingly higher quality representations of the visual world, there have not been commensurate advances in learning spatial auditory representations. To address this gap, we introduce Neural Acoustic Fields (NAFs), an implicit representation that captures how sounds propagate in a physical scene. By modeling acoustic propagation in a scene as a linear time-invariant system, NAFs learn to continuously map all emitter and listener location pairs to a neural impulse response function that can then be applied to arbitrary sounds. We demonstrate that the continuous nature of NAFs enables us to render spatial acoustics for a listener at an arbitrary location, and can predict sound propagation at novel locations. We further show that the representation learned by NAFs can help improve visual learning with sparse views. Finally, we show that a representation informative of scene structure emerges during the learning of NAFs.

The incredible success of transformers on sequence modeling tasks can be largely attributed to the self-attention mechanism, which allows information to be transferred between different parts of a sequence. Self-attention allows transformers to encode causal structure which makes them particularly suitable for sequence modeling. However, the process by which transformers learn such causal structure via gradient-based training algorithms remains poorly understood. To better understand this process, we introduce an in-context learning task that requires learning latent causal structure. We prove that gradient descent on a simplified two-layer transformer learns to solve this task by encoding the latent causal graph in the first attention layer. The key insight of our proof is that the gradient of the attention matrix encodes the mutual information between tokens. As a consequence of the data processing inequality, the largest entries of this gradient correspond to edges in the latent causal graph. As a special case, when the sequences are generated from in-context Markov chains, we prove that transformers learn an induction head (Olsson et al., 2022). We confirm our theoretical findings by showing that transformers trained on our in-context learning task are able to recover a wide variety of causal structures.

Spatial understanding is essential for Multimodal Large Language Models (MLLMs) to support perception, reasoning, and planning in embodied environments. Despite recent progress, existing studies reveal that MLLMs still struggle with spatial understanding. However, existing research lacks a comprehensive and systematic evaluation of these limitations, often restricted to isolated scenarios, such as single-view or video. In this work, we present a systematic analysis of spatial understanding from both data and architectural perspectives across three representative scenarios: single-view, multi-view, and video. We propose a benchmark named MulSeT (Multi-view Spatial Understanding Tasks), and design a series of experiments to analyze the spatial reasoning capabilities of MLLMs. From the data perspective, the performance of spatial understanding converges quickly as the training data increases, and the upper bound is relatively low, especially for tasks that require spatial imagination. This indicates that merely expanding training data is insufficient to achieve satisfactory performance. From the architectural perspective, we find that spatial understanding relies more heavily on the positional encoding within the visual encoder than within the language model, in both cascaded and native MLLMs. Moreover, we explore reasoning injection and envision future improvements through architectural design to optimize spatial understanding. These insights shed light on the limitations of current MLLMs and suggest new directions for improving spatial reasoning capabilities through data scaling and architectural tuning.

Large Language Models (LLMs) encode behaviors such as refusal within their activation space, yet identifying these behaviors remains a significant challenge. Existing methods often rely on predefined refusal templates detectable in output tokens or require manual analysis. We introduce COSMIC (Cosine Similarity Metrics for Inversion of Concepts), an automated framework for direction selection that identifies viable steering directions and target layers using cosine similarity - entirely independent of model outputs. COSMIC achieves steering performance comparable to prior methods without requiring assumptions about a model's refusal behavior, such as the presence of specific refusal tokens. It reliably identifies refusal directions in adversarial settings and weakly aligned models, and is capable of steering such models toward safer behavior with minimal increase in false refusals, demonstrating robustness across a wide range of alignment conditions.

The ability to describe images with natural language sentences is the hallmark for image and language understanding. Such a system has wide ranging applications such as annotating images and using natural sentences to search for images.In this project we focus on the task of bidirectional image retrieval: such asystem is capable of retrieving an image based on a sentence (image search) andretrieve sentence based on an image query (image annotation). We present asystem based on a global ranking objective function which uses a combinationof convolutional neural networks (CNN) and multi layer perceptrons (MLP).It takes a pair of image and sentence and processes them in different channels,finally embedding it into a common multimodal vector space. These embeddingsencode abstract semantic information about the two inputs and can be comparedusing traditional information retrieval approaches. For each such pair, the modelreturns a score which is interpretted as a similarity metric. If this score is high,the image and sentence are likely to convey similar meaning, and if the score is low then they are likely not to. The visual input is modeled via deep convolutional neural network. On theother hand we explore three models for the textual module. The first one isbag of words with an MLP. The second one uses n-grams (bigram, trigrams,and a combination of trigram & skip-grams) with an MLP. The third is morespecialized deep network specific for modeling variable length sequences (SSE).We report comparable performance to recent work in the field, even though ouroverall model is simpler. We also show that the training time choice of how wecan generate our negative samples has a significant impact on performance, and can be used to specialize the bi-directional system in one particular task.

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

While explicit positional encodings such as RoPE are a primary source of positional information in Transformer decoders, the causal mask also provides positional information. In this work, we prove that the causal mask can induce position-dependent patterns in attention scores, even without parameters or causal dependency in the input. Our theoretical analysis indicates that the induced attention pattern tends to favor nearby query-key pairs, mirroring the behavior of common positional encodings. Empirical analysis confirms that trained models exhibit the same behavior, with learned parameters further amplifying these patterns. Notably, we found that the interaction of causal mask and RoPE distorts RoPE's relative attention score patterns into non-relative ones. We consistently observed this effect in modern large language models, suggesting the importance of considering the causal mask as a source of positional information alongside explicit positional encodings.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and improve them by replacing their conversion of neural features into group representations, with an optimization whose loss intuitively measures the distance between group orbits. This change makes our approach applicable to a broader range of matrix groups, such as the Lorentz group O(1, 3), than these two proposals. We experimentally show our method's competitiveness on the SO(2) image classification task, and also its increased generality on the task with O(1, 3). Our implementation will be made accessible at https://github.com/tiendatnguyen-vision/Orbit-symmetrize.

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.

We investigate applying audio manipulations using pretrained neural network-based autoencoders as an alternative to traditional signal processing methods, since the former may provide greater semantic or perceptual organization. To establish the potential of this approach, we first establish if representations from these models encode information about manipulations. We carry out experiments and produce visualizations using representations from two different pretrained autoencoders. Our findings indicate that, while some information about audio manipulations is encoded, this information is both limited and encoded in a non-trivial way. This is supported by our attempts to visualize these representations, which demonstrated that trajectories of representations for common manipulations are typically nonlinear and content dependent, even for linear signal manipulations. As a result, it is not yet clear how these pretrained autoencoders can be used to manipulate audio signals, however, our results indicate this may be due to the lack of disentanglement with respect to common audio manipulations.

Linear attention mechanisms have gained prominence in causal language models due to their linear computational complexity and enhanced speed. However, the inherent decay mechanism in linear attention presents challenges when applied to multi-dimensional sequence modeling tasks, such as image processing and multi-modal learning. In these scenarios, the utilization of sequential scanning to establish a global receptive field necessitates multiple scans for multi-dimensional data, thereby leading to inefficiencies. This paper identifies the inefficiency caused by a multiplicative linear recurrence and proposes an efficient alternative additive linear recurrence to avoid the issue, as it can handle multi-dimensional data within a single scan. We further develop an efficient multi-dimensional sequential modeling framework called LightNet based on the new recurrence. Moreover, we present two new multi-dimensional linear relative positional encoding methods, MD-TPE and MD-LRPE to enhance the model's ability to discern positional information in multi-dimensional scenarios. Our empirical evaluations across various tasks, including image classification, image generation, bidirectional language modeling, and autoregressive language modeling, demonstrate the efficacy of LightNet, showcasing its potential as a versatile and efficient solution for multi-dimensional sequential modeling.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

This is not a typical survey of world models; it is a guide for those who want to build worlds. We do not aim to catalog every paper that has ever mentioned a ``world model". Instead, we follow one clear road: from early masked models that unified representation learning across modalities, to unified architectures that share a single paradigm, then to interactive generative models that close the action-perception loop, and finally to memory-augmented systems that sustain consistent worlds over time. We bypass loosely related branches to focus on the core: the generative heart, the interactive loop, and the memory system. We show that this is the most promising path towards true world models.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.

While originally designed for unidirectional generative modeling, decoder-only large language models (LLMs) are increasingly being adapted for bidirectional modeling. However, unidirectional and bidirectional models are typically trained separately with distinct objectives (generation and representation learning). This separation overlooks the opportunity for developing a more versatile language model and for these objectives to complement each other. In this work, we propose MAGNET, a method for adapting decoder-only LLMs to generate robust representations and infill missing text spans. MAGNET employs three self-supervised training objectives and introduces an attention mechanism that combines bidirectional and causal attention, enabling unified training across all objectives. Our results demonstrate that LLMs adapted with MAGNET (1) surpass strong text encoders on token-level and sentence-level representation learning tasks, (2) generate contextually appropriate text infills by leveraging past and future contexts, (3) perform open-ended text generation without excessive repetition of words or phrases, and (4) preserve the knowledge and reasoning capability gained by the LLM during pretraining.

Image-to-fMRI encoding is important for both neuroscience research and practical applications. However, such "Brain-Encoders" have been typically trained per-subject and per fMRI-dataset, thus restricted to very limited training data. In this paper we propose a Universal Brain-Encoder, which can be trained jointly on data from many different subjects/datasets/machines. What makes this possible is our new voxel-centric Encoder architecture, which learns a unique "voxel-embedding" per brain-voxel. Our Encoder trains to predict the response of each brain-voxel on every image, by directly computing the cross-attention between the brain-voxel embedding and multi-level deep image features. This voxel-centric architecture allows the functional role of each brain-voxel to naturally emerge from the voxel-image cross-attention. We show the power of this approach to (i) combine data from multiple different subjects (a "Crowd of Brains") to improve each individual brain-encoding, (ii) quick & effective Transfer-Learning across subjects, datasets, and machines (e.g., 3-Tesla, 7-Tesla), with few training examples, and (iii) use the learned voxel-embeddings as a powerful tool to explore brain functionality (e.g., what is encoded where in the brain).

Multi-layer perceptrons (MLP) have proven to be effective scene encoders when combined with higher-dimensional projections of the input, commonly referred to as positional encoding. However, scenes with a wide frequency spectrum remain a challenge: choosing high frequencies for positional encoding introduces noise in low structure areas, while low frequencies result in poor fitting of detailed regions. To address this, we propose a progressive positional encoding, exposing a hierarchical MLP structure to incremental sets of frequency encodings. Our model accurately reconstructs scenes with wide frequency bands and learns a scene representation at progressive level of detail without explicit per-level supervision. The architecture is modular: each level encodes a continuous implicit representation that can be leveraged separately for its respective resolution, meaning a smaller network for coarser reconstructions. Experiments on several 2D and 3D datasets show improvements in reconstruction accuracy, representational capacity and training speed compared to baselines.

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.

The efficient coding hypothesis proposes that the response properties of sensory systems are adapted to the statistics of their inputs such that they capture maximal information about the environment, subject to biological constraints. While elegant, information theoretic properties are notoriously difficult to measure in practical settings or to employ as objective functions in optimization. This difficulty has necessitated that computational models designed to test the hypothesis employ several different information metrics ranging from approximations and lower bounds to proxy measures like reconstruction error. Recent theoretical advances have characterized a novel and ecologically relevant efficiency metric, the manifold capacity, which is the number of object categories that may be represented in a linearly separable fashion. However, calculating manifold capacity is a computationally intensive iterative procedure that until now has precluded its use as an objective. Here we outline the simplifying assumptions that allow manifold capacity to be optimized directly, yielding Maximum Manifold Capacity Representations (MMCR). The resulting method is closely related to and inspired by advances in the field of self supervised learning (SSL), and we demonstrate that MMCRs are competitive with state of the art results on standard SSL benchmarks. Empirical analyses reveal differences between MMCRs and representations learned by other SSL frameworks, and suggest a mechanism by which manifold compression gives rise to class separability. Finally we evaluate a set of SSL methods on a suite of neural predictivity benchmarks, and find MMCRs are higly competitive as models of the ventral stream.

Causal representation learning has showed a variety of settings in which we can disentangle latent variables with identifiability guarantees (up to some reasonable equivalence class). Common to all of these approaches is the assumption that (1) the latent variables are represented as d-dimensional vectors, and (2) that the observations are the output of some injective generative function of these latent variables. While these assumptions appear benign, we show that when the observations are of multiple objects, the generative function is no longer injective and disentanglement fails in practice. We can address this failure by combining recent developments in object-centric learning and causal representation learning. By modifying the Slot Attention architecture arXiv:2006.15055, we develop an object-centric architecture that leverages weak supervision from sparse perturbations to disentangle each object's properties. This approach is more data-efficient in the sense that it requires significantly fewer perturbations than a comparable approach that encodes to a Euclidean space and we show that this approach successfully disentangles the properties of a set of objects in a series of simple image-based disentanglement experiments.

Understanding the property of neural populations (or voxels) in the human brain can advance our comprehension of human perceptual and cognitive processing capabilities and contribute to developing brain-inspired computer models. Recent encoding models using deep neural networks (DNNs) have successfully predicted voxel-wise activity. However, interpreting the properties that explain voxel responses remains challenging because of the black-box nature of DNNs. As a solution, we propose LLM-assisted Visual Cortex Captioning (LaVCa), a data-driven approach that uses large language models (LLMs) to generate natural-language captions for images to which voxels are selective. By applying LaVCa for image-evoked brain activity, we demonstrate that LaVCa generates captions that describe voxel selectivity more accurately than the previously proposed method. Furthermore, the captions generated by LaVCa quantitatively capture more detailed properties than the existing method at both the inter-voxel and intra-voxel levels. Furthermore, a more detailed analysis of the voxel-specific properties generated by LaVCa reveals fine-grained functional differentiation within regions of interest (ROIs) in the visual cortex and voxels that simultaneously represent multiple distinct concepts. These findings offer profound insights into human visual representations by assigning detailed captions throughout the visual cortex while highlighting the potential of LLM-based methods in understanding brain representations. Please check out our webpage at https://sites.google.com/view/lavca-llm/

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.

Modern vision models have achieved remarkable success in benchmarks where local features provide critical information about the target. There is now a growing interest in solving tasks that require more global reasoning, where local features offer no significant information. These tasks are reminiscent of the connectivity tasks discussed by Minsky and Papert in 1969, which exposed the limitations of the perceptron model and contributed to the first AI winter. In this paper, we revisit such tasks by introducing four global visual benchmarks involving path findings and mazes. We show that: (1) although today's large vision models largely surpass the expressivity limitations of the early models, they still struggle with the learning efficiency; we put forward the "globality degree" notion to understand this limitation; (2) we then demonstrate that the picture changes and global reasoning becomes feasible with the introduction of "visual scratchpads"; similarly to the text scratchpads and chain-of-thoughts used in language models, visual scratchpads help break down global tasks into simpler ones; (3) we finally show that some scratchpads are better than others, in particular, "inductive scratchpads" that take steps relying on less information afford better out-of-distribution generalization and succeed for smaller model sizes.

Despite their remarkable capabilities, LLMs learn word representations that exhibit the undesirable yet poorly understood feature of anisotropy. In this paper, we argue that the second moment in Adam is a cause of anisotropic embeddings, and suggest a modified optimizer called Coupled Adam to mitigate the problem. Our experiments demonstrate that Coupled Adam significantly improves the quality of embeddings, while also leading to better upstream and downstream performance on large enough datasets.

Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this work, however, we explore surprising dissociations between representation and computation that may pose challenges for such efforts. We create datasets in which we attempt to match the computational role that different features play, while manipulating other properties of the features or the data. We train various deep learning architectures to compute these multiple abstract features about their inputs. We find that their learned feature representations are systematically biased towards representing some features more strongly than others, depending upon extraneous properties such as feature complexity, the order in which features are learned, and the distribution of features over the inputs. For example, features that are simpler to compute or learned first tend to be represented more strongly and densely than features that are more complex or learned later, even if all features are learned equally well. We also explore how these biases are affected by architectures, optimizers, and training regimes (e.g., in transformers, features decoded earlier in the output sequence also tend to be represented more strongly). Our results help to characterize the inductive biases of gradient-based representation learning. These results also highlight a key challenge for interpretability - or for comparing the representations of models and brains - disentangling extraneous biases from the computationally important aspects of a system's internal representations.

Neural network training can be accelerated when a learnable update rule is used in lieu of classic adaptive optimizers (e.g. Adam). However, learnable update rules can be costly and unstable to train and use. A simpler recently proposed approach to accelerate training is to use Adam for most of the optimization steps and periodically, only every few steps, nowcast (predict future) parameters. We improve this approach by Neuron interaction and Nowcasting (NiNo) networks. NiNo leverages neuron connectivity and graph neural networks to more accurately nowcast parameters by learning in a supervised way from a set of training trajectories over multiple tasks. We show that in some networks, such as Transformers, neuron connectivity is non-trivial. By accurately modeling neuron connectivity, we allow NiNo to accelerate Adam training by up to 50\% in vision and language tasks.

We analyse perception and memory, using mathematical models for knowledge graphs and tensors, to gain insights into the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of subject-predicate-object (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information ---the "blackboard", or the "canvas" of the brain--- and fourth, a working memory layer as a processing center and data buffer. We discuss the operations of the four layers and relate them to the global workspace theory. In a Bayesian brain interpretation, semantic memory defines the prior for observable triple statements. We propose that ---in evolution and during development--- semantic memory, episodic memory, and natural language evolved as emergent properties in agents' process to gain a deeper understanding of sensory information.

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (α-ReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d ll |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding objective, while the compositionality is implicitly imposed by the architectural or algorithmic bias in the encoder. This misalignment between auto-encoding objective and learning compositionality often results in failure of capturing meaningful object representations. In this study, we propose a novel objective that explicitly encourages compositionality of the representations. Built upon the existing object-centric learning framework (e.g., slot attention), our method incorporates additional constraints that an arbitrary mixture of object representations from two images should be valid by maximizing the likelihood of the composite data. We demonstrate that incorporating our objective to the existing framework consistently improves the objective-centric learning and enhances the robustness to the architectural choices.

Over the past decade, predictive modeling of neural responses in the primate visual system has advanced significantly, largely driven by various DNN approaches. These include models optimized directly for visual recognition, cross-modal alignment through contrastive objectives, neural response prediction from scratch, and large language model embeddings.Likewise, different readout mechanisms, ranging from fully linear to spatial-feature factorized methods have been explored for mapping network activations to neural responses. Despite the diversity of these approaches, it remains unclear which method performs best across different visual regions. In this study, we systematically compare these approaches for modeling the human visual system and investigate alternative strategies to improve response predictions. Our findings reveal that for early to mid-level visual areas, response-optimized models with visual inputs offer superior prediction accuracy, while for higher visual regions, embeddings from LLMs based on detailed contextual descriptions of images and task-optimized models pretrained on large vision datasets provide the best fit. Through comparative analysis of these modeling approaches, we identified three distinct regions in the visual cortex: one sensitive primarily to perceptual features of the input that are not captured by linguistic descriptions, another attuned to fine-grained visual details representing semantic information, and a third responsive to abstract, global meanings aligned with linguistic content. We also highlight the critical role of readout mechanisms, proposing a novel scheme that modulates receptive fields and feature maps based on semantic content, resulting in an accuracy boost of 3-23% over existing SOTAs for all models and brain regions. Together, these findings offer key insights into building more precise models of the visual system.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

We investigate the internal structure of language model computations using causal analysis and demonstrate two motifs: (1) a form of adaptive computation where ablations of one attention layer of a language model cause another layer to compensate (which we term the Hydra effect) and (2) a counterbalancing function of late MLP layers that act to downregulate the maximum-likelihood token. Our ablation studies demonstrate that language model layers are typically relatively loosely coupled (ablations to one layer only affect a small number of downstream layers). Surprisingly, these effects occur even in language models trained without any form of dropout. We analyse these effects in the context of factual recall and consider their implications for circuit-level attribution in language models.

Humans and animals have a rich and flexible understanding of the physical world, which enables them to infer the underlying dynamical trajectories of objects and events, plausible future states, and use that to plan and anticipate the consequences of actions. However, the neural mechanisms underlying these computations are unclear. We combine a goal-driven modeling approach with dense neurophysiological data and high-throughput human behavioral readouts to directly impinge on this question. Specifically, we construct and evaluate several classes of sensory-cognitive networks to predict the future state of rich, ethologically-relevant environments, ranging from self-supervised end-to-end models with pixel-wise or object-centric objectives, to models that future predict in the latent space of purely static image-based or dynamic video-based pretrained foundation models. We find strong differentiation across these model classes in their ability to predict neural and behavioral data both within and across diverse environments. In particular, we find that neural responses are currently best predicted by models trained to predict the future state of their environment in the latent space of pretrained foundation models optimized for dynamic scenes in a self-supervised manner. Notably, models that future predict in the latent space of video foundation models that are optimized to support a diverse range of sensorimotor tasks, reasonably match both human behavioral error patterns and neural dynamics across all environmental scenarios that we were able to test. Overall, these findings suggest that the neural mechanisms and behaviors of primate mental simulation are thus far most consistent with being optimized to future predict on dynamic, reusable visual representations that are useful for embodied AI more generally.

Despite their powerful chat, coding, and reasoning abilities, Large Language Models (LLMs) frequently hallucinate. Conventional wisdom suggests that hallucinations are a consequence of a balance between creativity and factuality, which can be mitigated, but not eliminated, by grounding the LLM in external knowledge sources. Through extensive systematic experiments, we show that these traditional approaches fail to explain why LLMs hallucinate in practice. Specifically, we show that LLMs augmented with a massive Mixture of Memory Experts (MoME) can easily memorize large datasets of random numbers. We corroborate these experimental findings with a theoretical construction showing that simple neural networks trained to predict the next token hallucinate when the training loss is above a threshold as it usually does in practice when training on internet scale data. We interpret our findings by comparing against traditional retrieval methods for mitigating hallucinations. We use our findings to design a first generation model for removing hallucinations -- Lamini-1 -- that stores facts in a massive mixture of millions of memory experts that are retrieved dynamically.

We argue that representations in AI models, particularly deep networks, are converging. First, we survey many examples of convergence in the literature: over time and across multiple domains, the ways by which different neural networks represent data are becoming more aligned. Next, we demonstrate convergence across data modalities: as vision models and language models get larger, they measure distance between datapoints in a more and more alike way. We hypothesize that this convergence is driving toward a shared statistical model of reality, akin to Plato's concept of an ideal reality. We term such a representation the platonic representation and discuss several possible selective pressures toward it. Finally, we discuss the implications of these trends, their limitations, and counterexamples to our analysis.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Convolutional Neural Networks (CNNs) are the go-to model for computer vision. Recently, attention-based networks, such as the Vision Transformer, have also become popular. In this paper we show that while convolutions and attention are both sufficient for good performance, neither of them are necessary. We present MLP-Mixer, an architecture based exclusively on multi-layer perceptrons (MLPs). MLP-Mixer contains two types of layers: one with MLPs applied independently to image patches (i.e. "mixing" the per-location features), and one with MLPs applied across patches (i.e. "mixing" spatial information). When trained on large datasets, or with modern regularization schemes, MLP-Mixer attains competitive scores on image classification benchmarks, with pre-training and inference cost comparable to state-of-the-art models. We hope that these results spark further research beyond the realms of well established CNNs and Transformers.

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.

Prompt learning has emerged as a powerful paradigm for adapting vision-language models such as CLIP to downstream tasks. However, existing methods often overfit to seen data, leading to significant performance degradation when generalizing to novel classes or unseen domains. To address this limitation, we propose DiSa, a Directional Saliency-Aware Prompt Learning framework that integrates two complementary regularization strategies to enhance generalization. First, our Cross-Interactive Regularization (CIR) fosters cross-modal alignment by enabling cooperative learning between prompted and frozen encoders. Within CIR, a saliency-aware masking strategy guides the image encoder to prioritize semantically critical image regions, reducing reliance on less informative patches. Second, we introduce a directional regularization strategy that aligns visual embeddings with class-wise prototype features in a directional manner to prioritize consistency in feature orientation over strict proximity. This approach ensures robust generalization by leveraging stable prototype directions derived from class-mean statistics. Extensive evaluations on 11 diverse image classification benchmarks demonstrate that DiSa consistently outperforms state-of-the-art prompt learning methods across various settings, including base-to-novel generalization, cross-dataset transfer, domain generalization, and few-shot learning.

The attention mechanism is a core primitive in modern large language models (LLMs) and AI more broadly. Since attention by itself is permutation-invariant, position encoding is essential for modeling structured domains such as language. Rotary position encoding (RoPE) has emerged as the de facto standard approach for position encoding and is part of many modern LLMs. However, in RoPE the key/query transformation between two elements in a sequence is only a function of their relative position and otherwise independent of the actual input. This limits the expressivity of RoPE-based transformers. This paper describes PaTH, a flexible data-dependent position encoding scheme based on accumulated products of Householder(like) transformations, where each transformation is data-dependent, i.e., a function of the input. We derive an efficient parallel algorithm for training through exploiting a compact representation of products of Householder matrices, and implement a FlashAttention-style blockwise algorithm that minimizes I/O cost. Across both targeted synthetic benchmarks and moderate-scale real-world language modeling experiments, we find that PaTH demonstrates superior performance compared to RoPE and other recent baselines.

Vision-Language Models (VLMs) excel at identifying and describing objects but struggle with spatial reasoning such as accurately understanding the relative positions of objects. Inspired by the dual-pathway (ventral-dorsal) model of human vision, we investigate why VLMs fail spatial tasks despite strong object recognition capabilities. Our interpretability-driven analysis reveals a critical underlying cause: vision embeddings in VLMs are treated primarily as semantic ``bag-of-tokens," overshadowing subtle yet crucial positional cues due to their disproportionately large embedding norms. We validate this insight through extensive diagnostic experiments, demonstrating minimal performance impact when token orders or fine-grained spatial details are removed. Guided by these findings, we propose simple, interpretable interventions, including normalizing vision embedding norms and extracting mid-layer spatially rich features, to restore spatial awareness. Empirical results on both our synthetic data and standard benchmarks demonstrate improved spatial reasoning capabilities, highlighting the value of interpretability-informed design choices. Our study not only uncovers fundamental limitations in current VLM architectures but also provides actionable insights for enhancing structured perception of visual scenes.

The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and complexity of the problem, this manual architecture exploration likely exceeds human design abilities. In this paper, we propose a principled approach, rooted in differentiable neural architecture search, to automatically define branching (tree-like) structures in the encoding stage of a multi-task neural network. To allow flexibility within resource-constrained environments, we introduce a proxyless, resource-aware loss that dynamically controls the model size. Evaluations across a variety of dense prediction tasks show that our approach consistently finds high-performing branching structures within limited resource budgets.

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

Understanding which information is encoded in deep models of spoken and written language has been the focus of much research in recent years, as it is crucial for debugging and improving these architectures. Most previous work has focused on probing for speaker characteristics, acoustic and phonological information in models of spoken language, and for syntactic information in models of written language. Here we focus on the encoding of syntax in several self-supervised and visually grounded models of spoken language. We employ two complementary probing methods, combined with baselines and reference representations to quantify the degree to which syntactic structure is encoded in the activations of the target models. We show that syntax is captured most prominently in the middle layers of the networks, and more explicitly within models with more parameters.

Quite surprisingly, exact maximum a posteriori (MAP) decoding of neural language generators frequently leads to low-quality results. Rather, most state-of-the-art results on language generation tasks are attained using beam search despite its overwhelmingly high search error rate. This implies that the MAP objective alone does not express the properties we desire in text, which merits the question: if beam search is the answer, what was the question? We frame beam search as the exact solution to a different decoding objective in order to gain insights into why high probability under a model alone may not indicate adequacy. We find that beam search enforces uniform information density in text, a property motivated by cognitive science. We suggest a set of decoding objectives that explicitly enforce this property and find that exact decoding with these objectives alleviates the problems encountered when decoding poorly calibrated language generation models. Additionally, we analyze the text produced using various decoding strategies and see that, in our neural machine translation experiments, the extent to which this property is adhered to strongly correlates with BLEU.

In this work we revisit the most fundamental building block in deep learning, the multi-layer perceptron (MLP), and study the limits of its performance on vision tasks. Empirical insights into MLPs are important for multiple reasons. (1) Given the recent narrative "less inductive bias is better", popularized due to transformers eclipsing convolutional models, it is natural to explore the limits of this hypothesis. To that end, MLPs offer an ideal test bed, being completely free of any inductive bias. (2) MLPs have almost exclusively been the main protagonist in the deep learning theory literature due to their mathematical simplicity, serving as a proxy to explain empirical phenomena observed for more complex architectures. Surprisingly, experimental datapoints for MLPs are very difficult to find in the literature, especially when coupled with large pre-training protocols. This discrepancy between practice and theory is worrying: Do MLPs reflect the empirical advances exhibited by practical models? Or do theorists need to rethink the role of MLPs as a proxy? We provide insights into both these aspects. We show that the performance of MLPs drastically improves with scale (93% on CIFAR10, 79% on CIFAR100, 69% on TinyImageNet), highlighting that lack of inductive bias can indeed be compensated. We observe that MLPs mimic the behaviour of their modern counterparts faithfully, with some components in the learning setting however surprisingly exhibiting stronger or unexpected behaviours. Due to their inherent computational efficiency, large pre-training experiments become more accessible for academic researchers. All of our experiments were run on a single GPU.

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. In this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

We address prevailing challenges of the brain-powered research, departing from the observation that the literature hardly recover accurate spatial information and require subject-specific models. To address these challenges, we propose UMBRAE, a unified multimodal decoding of brain signals. First, to extract instance-level conceptual and spatial details from neural signals, we introduce an efficient universal brain encoder for multimodal-brain alignment and recover object descriptions at multiple levels of granularity from subsequent multimodal large language model (MLLM). Second, we introduce a cross-subject training strategy mapping subject-specific features to a common feature space. This allows a model to be trained on multiple subjects without extra resources, even yielding superior results compared to subject-specific models. Further, we demonstrate this supports weakly-supervised adaptation to new subjects, with only a fraction of the total training data. Experiments demonstrate that UMBRAE not only achieves superior results in the newly introduced tasks but also outperforms methods in well established tasks. To assess our method, we construct and share with the community a comprehensive brain understanding benchmark BrainHub. Our code and benchmark are available at https://weihaox.github.io/UMBRAE.

We present the Brain Treebank, a large-scale dataset of electrophysiological neural responses, recorded from intracranial probes while 10 subjects watched one or more Hollywood movies. Subjects watched on average 2.6 Hollywood movies, for an average viewing time of 4.3 hours, and a total of 43 hours. The audio track for each movie was transcribed with manual corrections. Word onsets were manually annotated on spectrograms of the audio track for each movie. Each transcript was automatically parsed and manually corrected into the universal dependencies (UD) formalism, assigning a part of speech to every word and a dependency parse to every sentence. In total, subjects heard over 38,000 sentences (223,000 words), while they had on average 168 electrodes implanted. This is the largest dataset of intracranial recordings featuring grounded naturalistic language, one of the largest English UD treebanks in general, and one of only a few UD treebanks aligned to multimodal features. We hope that this dataset serves as a bridge between linguistic concepts, perception, and their neural representations. To that end, we present an analysis of which electrodes are sensitive to language features while also mapping out a rough time course of language processing across these electrodes. The Brain Treebank is available at https://BrainTreebank.dev/

Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed-generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal.

The goal of this work is to characterize the representational impact that foveation operations have for machine vision systems, inspired by the foveated human visual system, which has higher acuity at the center of gaze and texture-like encoding in the periphery. To do so, we introduce models consisting of a first-stage fixed image transform followed by a second-stage learnable convolutional neural network, and we varied the first stage component. The primary model has a foveated-textural input stage, which we compare to a model with foveated-blurred input and a model with spatially-uniform blurred input (both matched for perceptual compression), and a final reference model with minimal input-based compression. We find that: 1) the foveated-texture model shows similar scene classification accuracy as the reference model despite its compressed input, with greater i.i.d. generalization than the other models; 2) the foveated-texture model has greater sensitivity to high-spatial frequency information and greater robustness to occlusion, w.r.t the comparison models; 3) both the foveated systems, show a stronger center image-bias relative to the spatially-uniform systems even with a weight sharing constraint. Critically, these results are preserved over different classical CNN architectures throughout their learning dynamics. Altogether, this suggests that foveation with peripheral texture-based computations yields an efficient, distinct, and robust representational format of scene information, and provides symbiotic computational insight into the representational consequences that texture-based peripheral encoding may have for processing in the human visual system, while also potentially inspiring the next generation of computer vision models via spatially-adaptive computation. Code + Data available here: https://github.com/ArturoDeza/EmergentProperties

Recently, polar-based representation has shown promising properties in perceptual tasks. In addition to Cartesian-based approaches, which separate point clouds unevenly, representing point clouds as polar grids has been recognized as an alternative due to (1) its advantage in robust performance under different resolutions and (2) its superiority in streaming-based approaches. However, state-of-the-art polar-based detection methods inevitably suffer from the feature distortion problem because of the non-uniform division of polar representation, resulting in a non-negligible performance gap compared to Cartesian-based approaches. To tackle this issue, we present PARTNER, a novel 3D object detector in the polar coordinate. PARTNER alleviates the dilemma of feature distortion with global representation re-alignment and facilitates the regression by introducing instance-level geometric information into the detection head. Extensive experiments show overwhelming advantages in streaming-based detection and different resolutions. Furthermore, our method outperforms the previous polar-based works with remarkable margins of 3.68% and 9.15% on Waymo and ONCE validation set, thus achieving competitive results over the state-of-the-art methods.

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

Understanding the hidden mechanisms behind human's visual perception is a fundamental question in neuroscience. To that end, investigating into the neural responses of human mind activities, such as functional Magnetic Resonance Imaging (fMRI), has been a significant research vehicle. However, analyzing fMRI signals is challenging, costly, daunting, and demanding for professional training. Despite remarkable progress in fMRI analysis, existing approaches are limited to generating 2D images and far away from being biologically meaningful and practically useful. Under this insight, we propose to generate visually plausible and functionally more comprehensive 3D outputs decoded from brain signals, enabling more sophisticated modeling of fMRI data. Conceptually, we reformulate this task as a {\em fMRI conditioned 3D object generation} problem. We design a novel 3D object representation learning method, Brain3D, that takes as input the fMRI data of a subject who was presented with a 2D image, and yields as output the corresponding 3D object images. The key capabilities of this model include tackling the noises with high-level semantic signals and a two-stage architecture design for progressive high-level information integration. Extensive experiments validate the superior capability of our model over previous state-of-the-art 3D object generation methods. Importantly, we show that our model captures the distinct functionalities of each region of human vision system as well as their intricate interplay relationships, aligning remarkably with the established discoveries in neuroscience. Further, preliminary evaluations indicate that Brain3D can successfully identify the disordered brain regions in simulated scenarios, such as V1, V2, V3, V4, and the medial temporal lobe (MTL) within the human visual system. Our data and code will be available at https://brain-3d.github.io/.

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.

The raster-ordered image token sequence exhibits a significant Euclidean distance between index-adjacent tokens at line breaks, making it unsuitable for autoregressive generation. To address this issue, this paper proposes Direction-Aware Diagonal Autoregressive Image Generation (DAR) method, which generates image tokens following a diagonal scanning order. The proposed diagonal scanning order ensures that tokens with adjacent indices remain in close proximity while enabling causal attention to gather information from a broader range of directions. Additionally, two direction-aware modules: 4D-RoPE and direction embeddings are introduced, enhancing the model's capability to handle frequent changes in generation direction. To leverage the representational capacity of the image tokenizer, we use its codebook as the image token embeddings. We propose models of varying scales, ranging from 485M to 2.0B. On the 256times256 ImageNet benchmark, our DAR-XL (2.0B) outperforms all previous autoregressive image generators, achieving a state-of-the-art FID score of 1.37.

Large language models based on transformers have achieved great empirical successes. However, as they are deployed more widely, there is a growing need to better understand their internal mechanisms in order to make them more reliable. These models appear to store vast amounts of knowledge from their training data, and to adapt quickly to new information provided in their context or prompt. We study how transformers balance these two types of knowledge by considering a synthetic setup where tokens are generated from either global or context-specific bigram distributions. By a careful empirical analysis of the training process on a simplified two-layer transformer, we illustrate the fast learning of global bigrams and the slower development of an "induction head" mechanism for the in-context bigrams. We highlight the role of weight matrices as associative memories, provide theoretical insights on how gradients enable their learning during training, and study the role of data-distributional properties.

Spiking neural networks (SNNs) offer both compelling potential advantages, including energy efficiency and low latencies and challenges including the non-differentiable nature of event spikes. Much of the initial research in this area has converted deep neural networks to equivalent SNNs, but this conversion approach potentially negates some of the advantages of SNN-based approaches developed from scratch. One promising area for high-performance SNNs is template matching and image recognition. This research introduces the first high-performance SNN for the Visual Place Recognition (VPR) task: given a query image, the SNN has to find the closest match out of a list of reference images. At the core of this new system is a novel assignment scheme that implements a form of ambiguity-informed salience, by up-weighting single-place-encoding neurons and down-weighting "ambiguous" neurons that respond to multiple different reference places. In a range of experiments on the challenging Nordland, Oxford RobotCar, SPEDTest, Synthia, and St Lucia datasets, we show that our SNN achieves comparable VPR performance to state-of-the-art and classical techniques, and degrades gracefully in performance with an increasing number of reference places. Our results provide a significant milestone towards SNNs that can provide robust, energy-efficient, and low latency robot localization.

The truthfulness of existing explanation methods in authentically elucidating the underlying model's decision-making process has been questioned. Existing methods have deviated from faithfully representing the model, thus susceptible to adversarial attacks. To address this, we propose a novel eXplainable AI (XAI) method called SRD (Sharing Ratio Decomposition), which sincerely reflects the model's inference process, resulting in significantly enhanced robustness in our explanations. Different from the conventional emphasis on the neuronal level, we adopt a vector perspective to consider the intricate nonlinear interactions between filters. We also introduce an interesting observation termed Activation-Pattern-Only Prediction (APOP), letting us emphasize the importance of inactive neurons and redefine relevance encapsulating all relevant information including both active and inactive neurons. Our method, SRD, allows for the recursive decomposition of a Pointwise Feature Vector (PFV), providing a high-resolution Effective Receptive Field (ERF) at any layer.

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an up-convolutional neural network. We apply the method to shallow representations (HOG, SIFT, LBP), as well as to deep networks. For shallow representations our approach provides significantly better reconstructions than existing methods, revealing that there is surprisingly rich information contained in these features. Inverting a deep network trained on ImageNet provides several insights into the properties of the feature representation learned by the network. Most strikingly, the colors and the rough contours of an image can be reconstructed from activations in higher network layers and even from the predicted class probabilities.

We introduce a modality-agnostic neural compression algorithm based on a functional view of data and parameterised as an Implicit Neural Representation (INR). Bridging the gap between latent coding and sparsity, we obtain compact latent representations non-linearly mapped to a soft gating mechanism. This allows the specialisation of a shared INR network to each data item through subnetwork selection. After obtaining a dataset of such latent representations, we directly optimise the rate/distortion trade-off in a modality-agnostic space using neural compression. Variational Compression of Implicit Neural Representations (VC-INR) shows improved performance given the same representational capacity pre quantisation while also outperforming previous quantisation schemes used for other INR techniques. Our experiments demonstrate strong results over a large set of diverse modalities using the same algorithm without any modality-specific inductive biases. We show results on images, climate data, 3D shapes and scenes as well as audio and video, introducing VC-INR as the first INR-based method to outperform codecs as well-known and diverse as JPEG 2000, MP3 and AVC/HEVC on their respective modalities.

Current vision systems typically assign fixed-length representations to images, regardless of the information content. This contrasts with human intelligence - and even large language models - which allocate varying representational capacities based on entropy, context and familiarity. Inspired by this, we propose an approach to learn variable-length token representations for 2D images. Our encoder-decoder architecture recursively processes 2D image tokens, distilling them into 1D latent tokens over multiple iterations of recurrent rollouts. Each iteration refines the 2D tokens, updates the existing 1D latent tokens, and adaptively increases representational capacity by adding new tokens. This enables compression of images into a variable number of tokens, ranging from 32 to 256. We validate our tokenizer using reconstruction loss and FID metrics, demonstrating that token count aligns with image entropy, familiarity and downstream task requirements. Recurrent token processing with increasing representational capacity in each iteration shows signs of token specialization, revealing potential for object / part discovery.

Mapping behavioral actions to neural activity is a fundamental goal of neuroscience. As our ability to record large neural and behavioral data increases, there is growing interest in modeling neural dynamics during adaptive behaviors to probe neural representations. In particular, neural latent embeddings can reveal underlying correlates of behavior, yet, we lack non-linear techniques that can explicitly and flexibly leverage joint behavior and neural data. Here, we fill this gap with a novel method, CEBRA, that jointly uses behavioral and neural data in a hypothesis- or discovery-driven manner to produce consistent, high-performance latent spaces. We validate its accuracy and demonstrate our tool's utility for both calcium and electrophysiology datasets, across sensory and motor tasks, and in simple or complex behaviors across species. It allows for single and multi-session datasets to be leveraged for hypothesis testing or can be used label-free. Lastly, we show that CEBRA can be used for the mapping of space, uncovering complex kinematic features, and rapid, high-accuracy decoding of natural movies from visual cortex.

Understanding how the brain represents visual information is a fundamental challenge in neuroscience and artificial intelligence. While AI-driven decoding of neural data has provided insights into the human visual system, integrating multimodal neuroimaging signals, such as EEG, MEG, and fMRI, remains a critical hurdle due to their inherent spatiotemporal misalignment. Current approaches often analyze these modalities in isolation, limiting a holistic view of neural representation. In this study, we introduce BrainFLORA, a unified framework for integrating cross-modal neuroimaging data to construct a shared neural representation. Our approach leverages multimodal large language models (MLLMs) augmented with modality-specific adapters and task decoders, achieving state-of-the-art performance in joint-subject visual retrieval task and has the potential to extend multitasking. Combining neuroimaging analysis methods, we further reveal how visual concept representations align across neural modalities and with real world object perception. We demonstrate that the brain's structured visual concept representations exhibit an implicit mapping to physical-world stimuli, bridging neuroscience and machine learning from different modalities of neural imaging. Beyond methodological advancements, BrainFLORA offers novel implications for cognitive neuroscience and brain-computer interfaces (BCIs). Our code is available at https://github.com/ncclab-sustech/BrainFLORA.

This study examines the integration of Contrastive Predictive Coding (CPC) with Spiking Neural Networks (SNN). While CPC learns the predictive structure of data to generate meaningful representations, SNN mimics the computational processes of biological neural systems over time. In this study, the goal is to develop a predictive coding model with greater biological plausibility by processing inputs and outputs in a spike-based system. The proposed model was tested on the MNIST dataset and achieved a high classification rate in distinguishing positive sequential samples from non-sequential negative samples. The study demonstrates that CPC can be effectively combined with SNN, showing that an SNN trained for classification tasks can also function as an encoding mechanism. Project codes and detailed results can be accessed on our GitHub page: https://github.com/vnd-ogrenme/ongorusel-kodlama/tree/main/CPC_SNN

Modern large language models (LLMs) achieve impressive performance on some tasks, while exhibiting distinctly non-human-like behaviors on others. This raises the question of how well the LLM's learned representations align with human representations. In this work, we introduce a novel approach to study representation alignment: we adopt a method from research on activation steering to identify neurons responsible for specific concepts (e.g., ''cat'') and then analyze the corresponding activation patterns. We find that LLM representations captured this way closely align with human representations inferred from behavioral data, matching inter-human alignment levels. Our approach significantly outperforms the alignment captured by word embeddings, which have been the focus of prior work on human-LLM alignment. Additionally, our approach enables a more granular view of how LLMs represent concepts -- we show that LLMs organize concepts in a way that mirrors human concept organization.

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.

Understanding the functional organization of higher visual cortex is a central focus in neuroscience. Past studies have primarily mapped the visual and semantic selectivity of neural populations using hand-selected stimuli, which may potentially bias results towards pre-existing hypotheses of visual cortex functionality. Moving beyond conventional approaches, we introduce a data-driven method that generates natural language descriptions for images predicted to maximally activate individual voxels of interest. Our method -- Semantic Captioning Using Brain Alignments ("BrainSCUBA") -- builds upon the rich embedding space learned by a contrastive vision-language model and utilizes a pre-trained large language model to generate interpretable captions. We validate our method through fine-grained voxel-level captioning across higher-order visual regions. We further perform text-conditioned image synthesis with the captions, and show that our images are semantically coherent and yield high predicted activations. Finally, to demonstrate how our method enables scientific discovery, we perform exploratory investigations on the distribution of "person" representations in the brain, and discover fine-grained semantic selectivity in body-selective areas. Unlike earlier studies that decode text, our method derives voxel-wise captions of semantic selectivity. Our results show that BrainSCUBA is a promising means for understanding functional preferences in the brain, and provides motivation for further hypothesis-driven investigation of visual cortex.

Rotary Position Embedding (RoPE) has shown strong performance in text-based Large Language Models (LLMs), but extending it to video remains a challenge due to the intricate spatiotemporal structure of video frames. Existing adaptations, such as RoPE-3D, attempt to encode spatial and temporal dimensions separately but suffer from two major limitations: positional bias in attention distribution and disruptions in video-text transitions. To overcome these issues, we propose Video Rotary Position Embedding (VRoPE), a novel positional encoding method tailored for Video-LLMs. Our approach restructures positional indices to preserve spatial coherence and ensure a smooth transition between video and text tokens. Additionally, we introduce a more balanced encoding strategy that mitigates attention biases, ensuring a more uniform distribution of spatial focus. Extensive experiments on Vicuna and Qwen2 across different model scales demonstrate that VRoPE consistently outperforms previous RoPE variants, achieving significant improvements in video understanding, temporal reasoning, and retrieval tasks. Code will be available at https://github.com/johncaged/VRoPE

The mechanisms by which reasoning training reshapes LLMs' internal computations remain unclear. We study lightweight steering vectors inserted into the base model's residual stream and trained with a reinforcement-learning objective. These vectors match full fine-tuning performance while preserving the interpretability of small, additive interventions. Using logit-lens readouts and path-patching analyses on two models, we find that (i) the last-layer steering vector acts like a token-substitution bias concentrated on the first generated token, consistently boosting tokens such as "To" and "Step"; (ii) the penultimate-layer vector leaves attention patterns largely intact and instead operates through the MLP and unembedding, preferentially up-weighting process words and structure symbols; and (iii) middle layers de-emphasize non-English tokens. Next, we show that a SAE isolates features associated with correct generations. We also show that steering vectors (i) transfer to other models, (ii) combine across layers when trained in isolation, and (iii) concentrate magnitude on meaningful prompt segments under adaptive token-wise scaling. Taken together, these results deepen understanding of how trained steering vectors shape computation and should inform future work in activation engineering and the study of reasoning models.

We investigate the possibility of forcing a self-supervised model trained using a contrastive predictive loss to extract slowly varying latent representations. Rather than producing individual predictions for each of the future representations, the model emits a sequence of predictions shorter than that of the upcoming representations to which they will be aligned. In this way, the prediction network solves a simpler task of predicting the next symbols, but not their exact timing, while the encoding network is trained to produce piece-wise constant latent codes. We evaluate the model on a speech coding task and demonstrate that the proposed Aligned Contrastive Predictive Coding (ACPC) leads to higher linear phone prediction accuracy and lower ABX error rates, while being slightly faster to train due to the reduced number of prediction heads.

Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the lack of a regular and explicit grid structure also makes it challenging to apply generative modeling directly on implicit neural fields in order to synthesize new data. To this end, we propose HyperDiffusion, a novel approach for unconditional generative modeling of implicit neural fields. HyperDiffusion operates directly on MLP weights and generates new neural implicit fields encoded by synthesized MLP parameters. Specifically, a collection of MLPs is first optimized to faithfully represent individual data samples. Subsequently, a diffusion process is trained in this MLP weight space to model the underlying distribution of neural implicit fields. HyperDiffusion enables diffusion modeling over a implicit, compact, and yet high-fidelity representation of complex signals across 3D shapes and 4D mesh animations within one single unified framework.

Recent voxel-wise multimodal brain encoding studies have shown that multimodal large language models (MLLMs) exhibit a higher degree of brain alignment compared to unimodal models in both unimodal and multimodal stimulus settings. More recently, instruction-tuned multimodal models have shown to generate task-specific representations that align strongly with brain activity. However, prior work evaluating the brain alignment of MLLMs has primarily focused on unimodal settings or relied on non-instruction-tuned multimodal models for multimodal stimuli. To address this gap, we investigated brain alignment, that is, measuring the degree of predictivity of neural activity recorded while participants were watching naturalistic movies (video along with audio) with representations derived from MLLMs. We utilized instruction-specific embeddings from six video and two audio instruction-tuned MLLMs. Experiments with 13 video task-specific instructions show that instruction-tuned video MLLMs significantly outperform non-instruction-tuned multimodal (by 15%) and unimodal models (by 20%). Our evaluation of MLLMs for both video and audio tasks using language-guided instructions shows clear disentanglement in task-specific representations from MLLMs, leading to precise differentiation of multimodal functional processing in the brain. We also find that MLLM layers align hierarchically with the brain, with early sensory areas showing strong alignment with early layers, while higher-level visual and language regions align more with middle to late layers. These findings provide clear evidence for the role of task-specific instructions in improving the alignment between brain activity and MLLMs, and open new avenues for mapping joint information processing in both the systems. We make the code publicly available [https://github.com/subbareddy248/mllm_videos].

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types-such as neurons that activate when an operand falls within a certain range-and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a "bag of heuristics".

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Recent advances in Large Multimodal Models (LMMs) lead to significant breakthroughs in both academia and industry. One question that arises is how we, as humans, can understand their internal neural representations. This paper takes an initial step towards addressing this question by presenting a versatile framework to identify and interpret the semantics within LMMs. Specifically, 1) we first apply a Sparse Autoencoder(SAE) to disentangle the representations into human understandable features. 2) We then present an automatic interpretation framework to interpreted the open-semantic features learned in SAE by the LMMs themselves. We employ this framework to analyze the LLaVA-NeXT-8B model using the LLaVA-OV-72B model, demonstrating that these features can effectively steer the model's behavior. Our results contribute to a deeper understanding of why LMMs excel in specific tasks, including EQ tests, and illuminate the nature of their mistakes along with potential strategies for their rectification. These findings offer new insights into the internal mechanisms of LMMs and suggest parallels with the cognitive processes of the human brain.

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

Contemporary diffusion models built upon U-Net or Diffusion Transformer (DiT) architectures have revolutionized image generation through transformer-based attention mechanisms. The prevailing paradigm has commonly employed self-attention with quadratic computational complexity to handle global spatial relationships in complex images, thereby synthesizing high-fidelity images with coherent visual semantics.Contrary to conventional wisdom, our systematic layer-wise analysis reveals an interesting discrepancy: self-attention in pre-trained diffusion models predominantly exhibits localized attention patterns, closely resembling convolutional inductive biases. This suggests that global interactions in self-attention may be less critical than commonly assumed.Driven by this, we propose \(\Delta\)ConvFusion to replace conventional self-attention modules with Pyramid Convolution Blocks (\(\Delta\)ConvBlocks).By distilling attention patterns into localized convolutional operations while keeping other components frozen, \(\Delta\)ConvFusion achieves performance comparable to transformer-based counterparts while reducing computational cost by 6929times and surpassing LinFusion by 5.42times in efficiency--all without compromising generative fidelity.

Much of the excitement in modern AI is driven by the observation that scaling up existing systems leads to better performance. But does better performance necessarily imply better internal representations? While the representational optimist assumes it must, this position paper challenges that view. We compare neural networks evolved through an open-ended search process to networks trained via conventional stochastic gradient descent (SGD) on the simple task of generating a single image. This minimal setup offers a unique advantage: each hidden neuron's full functional behavior can be easily visualized as an image, thus revealing how the network's output behavior is internally constructed neuron by neuron. The result is striking: while both networks produce the same output behavior, their internal representations differ dramatically. The SGD-trained networks exhibit a form of disorganization that we term fractured entangled representation (FER). Interestingly, the evolved networks largely lack FER, even approaching a unified factored representation (UFR). In large models, FER may be degrading core model capacities like generalization, creativity, and (continual) learning. Therefore, understanding and mitigating FER could be critical to the future of representation learning.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the line graph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. Code and Datasets are available at: https://github.com/ml-jku/plstm_experiments.

Recent advances in Graph Neural Networks (GNNs) and Graph Transformers (GTs) have been driven by innovations in architectures and Positional Encodings (PEs), which are critical for augmenting node features and capturing graph topology. PEs are essential for GTs, where topological information would otherwise be lost without message-passing. However, PEs are often tested alongside novel architectures, making it difficult to isolate their effect on established models. To address this, we present a comprehensive benchmark of PEs in a unified framework that includes both message-passing GNNs and GTs. We also establish theoretical connections between MPNNs and GTs and introduce a sparsified GRIT attention mechanism to examine the influence of global connectivity. Our findings demonstrate that previously untested combinations of GNN architectures and PEs can outperform existing methods and offer a more comprehensive picture of the state-of-the-art. To support future research and experimentation in our framework, we make the code publicly available.

Despite their impressive capabilities, multimodal large language models (MLLMs) are prone to hallucinations, i.e., the generated content that is nonsensical or unfaithful to input sources. Unlike in LLMs, hallucinations in MLLMs often stem from the sensitivity of text decoder to visual tokens, leading to a phenomenon akin to "amnesia" about visual information. To address this issue, we propose MemVR, a novel decoding paradigm inspired by common cognition: when the memory of an image seen the moment before is forgotten, people will look at it again for factual answers. Following this principle, we treat visual tokens as supplementary evidence, re-injecting them into the MLLM through Feed Forward Network (FFN) as "key-value memory" at the middle trigger layer. This "look-twice" mechanism occurs when the model exhibits high uncertainty during inference, effectively enhancing factual alignment. Comprehensive experimental evaluations demonstrate that MemVR significantly mitigates hallucination across various MLLMs and excels in general benchmarks without incurring additional time overhead. The implementation is available from https://github.com/1zhou-Wang/MemVR

Language models strongly rely on frequency information because they maximize the likelihood of tokens during pre-training. As a consequence, language models tend to not generalize well to tokens that are seldom seen during training. Moreover, maximum likelihood training has been discovered to give rise to anisotropy: representations of tokens in a model tend to cluster tightly in a high-dimensional cone, rather than spreading out over their representational capacity. Our work introduces a method for quantifying the frequency bias of a language model by assessing sentence-level perplexity with respect to token-level frequency. We then present a method for reducing the frequency bias of a language model by inducing a syntactic prior over token representations during pre-training. Our Syntactic Smoothing method adjusts the maximum likelihood objective function to distribute the learning signal to syntactically similar tokens. This approach results in better performance on infrequent English tokens and a decrease in anisotropy. We empirically show that the degree of anisotropy in a model correlates with its frequency bias.

Some neurons in deep networks specialize in recognizing highly specific perceptual, structural, or semantic features of inputs. In computer vision, techniques exist for identifying neurons that respond to individual concept categories like colors, textures, and object classes. But these techniques are limited in scope, labeling only a small subset of neurons and behaviors in any network. Is a richer characterization of neuron-level computation possible? We introduce a procedure (called MILAN, for mutual-information-guided linguistic annotation of neurons) that automatically labels neurons with open-ended, compositional, natural language descriptions. Given a neuron, MILAN generates a description by searching for a natural language string that maximizes pointwise mutual information with the image regions in which the neuron is active. MILAN produces fine-grained descriptions that capture categorical, relational, and logical structure in learned features. These descriptions obtain high agreement with human-generated feature descriptions across a diverse set of model architectures and tasks, and can aid in understanding and controlling learned models. We highlight three applications of natural language neuron descriptions. First, we use MILAN for analysis, characterizing the distribution and importance of neurons selective for attribute, category, and relational information in vision models. Second, we use MILAN for auditing, surfacing neurons sensitive to human faces in datasets designed to obscure them. Finally, we use MILAN for editing, improving robustness in an image classifier by deleting neurons sensitive to text features spuriously correlated with class labels.

Multimodal large language models (MLLMs) face an inherent trade-off between faithfulness and creativity, as different tasks require varying degrees of associative reasoning. However, existing methods lack the flexibility to modulate this reasoning strength, limiting MLLMs' adaptability across factual and creative scenarios. To bridge this gap, we propose equipping MLLMs with mechanisms that enable flexible control over associative reasoning. We begin by investigating the internal mechanisms underlying associative behavior in MLLMs and find that: (1) middle layers play a pivotal role in shaping model's associative tendencies, (2) modifying representations in these layers effectively regulates associative reasoning strength, and (3) hallucinations can be exploited to derive steering vectors that guide this modulation. Building on these findings, we introduce Flexible Association Control (FlexAC), a lightweight and training-free framework for modulating associative behavior in MLLMs. FlexAC first induces hallucination-guided intermediate representations to encode associative directions. Then, it selects high-association instances to construct effective associative steering vectors, whose strengths are adaptively calibrated to balance creative guidance with output stability. Finally, recognizing the multi-dimensional nature of associative reasoning, FlexAC incorporates task-specific associative vectors derived from a forward pass on a few target-domain samples, enabling models to follow diverse associative directions and better adapt to creative tasks. Notably, our method achieves up to a 5.8x improvement in creativity on Creation-MMBench and a 29% reduction in hallucination rate on CHAIR, surpassing existing baselines and demonstrating its effectiveness in enabling flexible control over associative reasoning in MLLMs. Our code is available at https://github.com/ylhz/FlexAC.

Biological systems perceive the world by simultaneously processing high-dimensional inputs from modalities as diverse as vision, audition, touch, proprioception, etc. The perception models used in deep learning on the other hand are designed for individual modalities, often relying on domain-specific assumptions such as the local grid structures exploited by virtually all existing vision models. These priors introduce helpful inductive biases, but also lock models to individual modalities. In this paper we introduce the Perceiver - a model that builds upon Transformers and hence makes few architectural assumptions about the relationship between its inputs, but that also scales to hundreds of thousands of inputs, like ConvNets. The model leverages an asymmetric attention mechanism to iteratively distill inputs into a tight latent bottleneck, allowing it to scale to handle very large inputs. We show that this architecture is competitive with or outperforms strong, specialized models on classification tasks across various modalities: images, point clouds, audio, video, and video+audio. The Perceiver obtains performance comparable to ResNet-50 and ViT on ImageNet without 2D convolutions by directly attending to 50,000 pixels. It is also competitive in all modalities in AudioSet.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by quantizing their continuous features into what we call codebook features. Codebook features are produced by finetuning neural networks with vector quantization bottlenecks at each layer, producing a network whose hidden features are the sum of a small number of discrete vector codes chosen from a larger codebook. Surprisingly, we find that neural networks can operate under this extreme bottleneck with only modest degradation in performance. This sparse, discrete bottleneck also provides an intuitive way of controlling neural network behavior: first, find codes that activate when the desired behavior is present, then activate those same codes during generation to elicit that behavior. We validate our approach by training codebook Transformers on several different datasets. First, we explore a finite state machine dataset with far more hidden states than neurons. In this setting, our approach overcomes the superposition problem by assigning states to distinct codes, and we find that we can make the neural network behave as if it is in a different state by activating the code for that state. Second, we train Transformer language models with up to 410M parameters on two natural language datasets. We identify codes in these models representing diverse, disentangled concepts (ranging from negative emotions to months of the year) and find that we can guide the model to generate different topics by activating the appropriate codes during inference. Overall, codebook features appear to be a promising unit of analysis and control for neural networks and interpretability. Our codebase and models are open-sourced at https://github.com/taufeeque9/codebook-features.

Vision-Language Models (VLMs) have shown remarkable performance in integrating visual and textual information for tasks such as image captioning and visual question answering. However, these models struggle with compositional generalization and object binding, which limit their ability to handle novel combinations of objects and their attributes. Our work explores the root causes of these failures using mechanistic interpretability techniques. We show evidence that individual neurons in the MLP layers of CLIP's vision encoder represent multiple features, and this "superposition" directly hinders its compositional feature representation which consequently affects compositional reasoning and object binding capabilities. We hope this study will serve as an initial step toward uncovering the mechanistic roots of compositional failures in VLMs. The code and supporting results can be found https://github.com/Mystic-Slice/Do-VLMs-Have-Bad-Eyes .

The representation degeneration problem is a phenomenon that is widely observed among self-supervised learning methods based on Transformers. In NLP, it takes the form of anisotropy, a singular property of hidden representations which makes them unexpectedly close to each other in terms of angular distance (cosine-similarity). Some recent works tend to show that anisotropy is a consequence of optimizing the cross-entropy loss on long-tailed distributions of tokens. We show in this paper that anisotropy can also be observed empirically in language models with specific objectives that should not suffer directly from the same consequences. We also show that the anisotropy problem extends to Transformers trained on other modalities. Our observations suggest that anisotropy is actually inherent to Transformers-based models.

There is a growing interest in learning data representations that work well for many different types of problems and data. In this paper, we look in particular at the task of learning a single visual representation that can be successfully utilized in the analysis of very different types of images, from dog breeds to stop signs and digits. Inspired by recent work on learning networks that predict the parameters of another, we develop a tunable deep network architecture that, by means of adapter residual modules, can be steered on the fly to diverse visual domains. Our method achieves a high degree of parameter sharing while maintaining or even improving the accuracy of domain-specific representations. We also introduce the Visual Decathlon Challenge, a benchmark that evaluates the ability of representations to capture simultaneously ten very different visual domains and measures their ability to recognize well uniformly.

Current vision models typically maintain a fixed correspondence between their representation structure and image space. Each layer comprises a set of tokens arranged "on-the-grid," which biases patches or tokens to encode information at a specific spatio(-temporal) location. In this work we present Moving Off-the-Grid (MooG), a self-supervised video representation model that offers an alternative approach, allowing tokens to move "off-the-grid" to better enable them to represent scene elements consistently, even as they move across the image plane through time. By using a combination of cross-attention and positional embeddings we disentangle the representation structure and image structure. We find that a simple self-supervised objective--next frame prediction--trained on video data, results in a set of latent tokens which bind to specific scene structures and track them as they move. We demonstrate the usefulness of MooG's learned representation both qualitatively and quantitatively by training readouts on top of the learned representation on a variety of downstream tasks. We show that MooG can provide a strong foundation for different vision tasks when compared to "on-the-grid" baselines.

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.

We explore different ways to utilize position-based cross-attention in seq2seq networks to enable length generalization in algorithmic tasks. We show that a simple approach of interpolating the original and reversed encoded representations combined with relative attention allows near-perfect length generalization for both forward and reverse lookup tasks or copy tasks that had been generally hard to tackle. We also devise harder diagnostic tasks where the relative distance of the ideal attention position varies with timestep. In such settings, the simple interpolation trick with relative attention is not sufficient. We introduce novel variants of location attention building on top of Dubois et al. (2020) to address the new diagnostic tasks. We also show the benefits of our approaches for length generalization in SCAN (Lake & Baroni, 2018) and CFQ (Keysers et al., 2020). Our code is available on GitHub.

Implicit Neural Representations (INRs) and Neural Fields are a novel paradigm for signal representation, from images and audio to 3D scenes and videos. The fundamental idea is to represent a signal as a continuous and differentiable neural network. This idea offers unprecedented benefits such as continuous resolution and memory efficiency, enabling new compression techniques. However, representing data as neural networks poses new challenges. For instance, given a 2D image as a neural network, how can we further compress such a neural image?. In this work, we present a novel analysis on compressing neural fields, with the focus on images. We also introduce Adaptive Neural Images (ANI), an efficient neural representation that enables adaptation to different inference or transmission requirements. Our proposed method allows to reduce the bits-per-pixel (bpp) of the neural image by 4x, without losing sensitive details or harming fidelity. We achieve this thanks to our successful implementation of 4-bit neural representations. Our work offers a new framework for developing compressed neural fields.

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model - without any task boundaries - reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

Multimodal learning enhances the perceptual capabilities of cognitive systems by integrating information from different sensory modalities. However, existing multimodal fusion research typically assumes static integration, not fully incorporating key dynamic mechanisms found in the brain. Specifically, the brain exhibits an inverse effectiveness phenomenon, wherein weaker unimodal cues yield stronger multisensory integration benefits; conversely, when individual modal cues are stronger, the effect of fusion is diminished. This mechanism enables biological systems to achieve robust cognition even with scarce or noisy perceptual cues. Inspired by this biological mechanism, we explore the relationship between multimodal output and information from individual modalities, proposing an inverse effectiveness driven multimodal fusion (IEMF) strategy. By incorporating this strategy into neural networks, we achieve more efficient integration with improved model performance and computational efficiency, demonstrating up to 50% reduction in computational cost across diverse fusion methods. We conduct experiments on audio-visual classification, continual learning, and question answering tasks to validate our method. Results consistently demonstrate that our method performs excellently in these tasks. To verify universality and generalization, we also conduct experiments on Artificial Neural Networks (ANN) and Spiking Neural Networks (SNN), with results showing good adaptability to both network types. Our research emphasizes the potential of incorporating biologically inspired mechanisms into multimodal networks and provides promising directions for the future development of multimodal artificial intelligence. The code is available at https://github.com/Brain-Cog-Lab/IEMF.

Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.

We develop a novel bi-directional attention model for dependency parsing, which learns to agree on headword predictions from the forward and backward parsing directions. The parsing procedure for each direction is formulated as sequentially querying the memory component that stores continuous headword embeddings. The proposed parser makes use of {\it soft} headword embeddings, allowing the model to implicitly capture high-order parsing history without dramatically increasing the computational complexity. We conduct experiments on English, Chinese, and 12 other languages from the CoNLL 2006 shared task, showing that the proposed model achieves state-of-the-art unlabeled attachment scores on 6 languages.

In this paper, we give an in-depth analysis on the mathematical problem formulations and the probabilistic optimization explorations for some of the key components in Transformer model [33] in the field of generative AI. We explore and discuss some potential further enhancement for current state of the art methods for some key underlying technologies of generative AI models from algorithmic and probabilistic optimization perspective. In particular, we present an optimal solution for sub-word encoding (SWE) based on similar initial settings as that of byte-pair encoding (BPE) algorithm in [9] with similar objectives as that of WordPiece approach in [28, 31] to maximize the likelihood of the training data. We also present cross entropy optimization method to optimize hyperparameters for word2vec model [17]. In addition, we propose a factored combination of rotary positional encoding (RoPE) [32] and attention with linear biases (ALiBi) [23] with a harmonic series. We also present a probabilistic FlashAttention [6, 7] (PrFlashAttention) method with a probability distribution over block distances in the matrix to decide which block is likely to participate in a given round of attention computation while maintaining the lower triangle shape of the tensor for autoregressive language models by re-shaping the tensors. Finally, we present staircase adaptive quantization (SAQ) of key-value (KV) cache for multi-query attention (MQA) based on the framework presented in [16] to have gradual quantization degradation while achieving reasonable model quality and cost savings.

Invasive brain-computer interfaces have garnered significant attention due to their high performance. The current intracranial stereoElectroEncephaloGraphy (sEEG) foundation models typically build univariate representations based on a single channel. Some of them further use Transformer to model the relationship among channels. However, due to the locality and specificity of brain computation, their performance on more difficult tasks, e.g., speech decoding, which demands intricate processing in specific brain regions, is yet to be fully investigated. We hypothesize that building multi-variate representations within certain brain regions can better capture the specific neural processing. To explore this hypothesis, we collect a well-annotated Chinese word-reading sEEG dataset, targeting language-related brain networks, over 12 subjects. Leveraging this benchmark dataset, we developed the Du-IN model that can extract contextual embeddings from specific brain regions through discrete codebook-guided mask modeling. Our model achieves SOTA performance on the downstream 61-word classification task, surpassing all baseline models. Model comparison and ablation analysis reveal that our design choices, including (i) multi-variate representation by fusing channels in vSMC and STG regions and (ii) self-supervision by discrete codebook-guided mask modeling, significantly contribute to these performances. Collectively, our approach, inspired by neuroscience findings, capitalizing on multi-variate neural representation from specific brain regions, is suitable for invasive brain modeling. It marks a promising neuro-inspired AI approach in BCI.

Information flows by routes inside the network via mechanisms implemented in the model. These routes can be represented as graphs where nodes correspond to token representations and edges to operations inside the network. We automatically build these graphs in a top-down manner, for each prediction leaving only the most important nodes and edges. In contrast to the existing workflows relying on activation patching, we do this through attribution: this allows us to efficiently uncover existing circuits with just a single forward pass. Additionally, the applicability of our method is far beyond patching: we do not need a human to carefully design prediction templates, and we can extract information flow routes for any prediction (not just the ones among the allowed templates). As a result, we can talk about model behavior in general, for specific types of predictions, or different domains. We experiment with Llama 2 and show that the role of some attention heads is overall important, e.g. previous token heads and subword merging heads. Next, we find similarities in Llama 2 behavior when handling tokens of the same part of speech. Finally, we show that some model components can be specialized on domains such as coding or multilingual texts.

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

Most of the recent works on probing representations have focused on BERT, with the presumption that the findings might be similar to the other models. In this work, we extend the probing studies to two other models in the family, namely ELECTRA and XLNet, showing that variations in the pre-training objectives or architectural choices can result in different behaviors in encoding linguistic information in the representations. Most notably, we observe that ELECTRA tends to encode linguistic knowledge in the deeper layers, whereas XLNet instead concentrates that in the earlier layers. Also, the former model undergoes a slight change during fine-tuning, whereas the latter experiences significant adjustments. Moreover, we show that drawing conclusions based on the weight mixing evaluation strategy -- which is widely used in the context of layer-wise probing -- can be misleading given the norm disparity of the representations across different layers. Instead, we adopt an alternative information-theoretic probing with minimum description length, which has recently been proven to provide more reliable and informative results.

Many AI models trained on natural images develop representations that resemble those of the human brain. However, the factors that drive this brain-model similarity remain poorly understood. To disentangle how the model, training and data independently lead a neural network to develop brain-like representations, we trained a family of self-supervised vision transformers (DINOv3) that systematically varied these different factors. We compare their representations of images to those of the human brain recorded with both fMRI and MEG, providing high resolution in spatial and temporal analyses. We assess the brain-model similarity with three complementary metrics focusing on overall representational similarity, topographical organization, and temporal dynamics. We show that all three factors - model size, training amount, and image type - independently and interactively impact each of these brain similarity metrics. In particular, the largest DINOv3 models trained with the most human-centric images reach the highest brain-similarity. This emergence of brain-like representations in AI models follows a specific chronology during training: models first align with the early representations of the sensory cortices, and only align with the late and prefrontal representations of the brain with considerably more training. Finally, this developmental trajectory is indexed by both structural and functional properties of the human cortex: the representations that are acquired last by the models specifically align with the cortical areas with the largest developmental expansion, thickness, least myelination, and slowest timescales. Overall, these findings disentangle the interplay between architecture and experience in shaping how artificial neural networks come to see the world as humans do, thus offering a promising framework to understand how the human brain comes to represent its visual world.

Vision-Language Models (VLMs) have recently demonstrated remarkable capabilities in comprehending complex visual content. However, the mechanisms underlying how VLMs process visual information remain largely unexplored. In this paper, we conduct a thorough empirical analysis, focusing on attention modules across layers. We reveal several key insights about how these models process visual data: (i) the internal representation of the query tokens (e.g., representations of "describe the image"), is utilized by VLMs to store global image information; we demonstrate that these models generate surprisingly descriptive responses solely from these tokens, without direct access to image tokens. (ii) Cross-modal information flow is predominantly influenced by the middle layers (approximately 25% of all layers), while early and late layers contribute only marginally.(iii) Fine-grained visual attributes and object details are directly extracted from image tokens in a spatially localized manner, i.e., the generated tokens associated with a specific object or attribute attend strongly to their corresponding regions in the image. We propose novel quantitative evaluation to validate our observations, leveraging real-world complex visual scenes. Finally, we demonstrate the potential of our findings in facilitating efficient visual processing in state-of-the-art VLMs.

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with H heads, dimension d, and context size n < d, featuring Theta(Hd^2) parameters, can memorize Omega(Hn) examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

Large language model (LLM)-based embedding models, benefiting from large scale pre-training and post-training, have begun to surpass BERT and T5-based models on general-purpose text embedding tasks such as document retrieval. However, a fundamental limitation of LLM embeddings lies in the unidirectional attention used during autoregressive pre-training, which misaligns with the bidirectional nature of text embedding tasks. To this end, We propose adopting diffusion language models for text embeddings, motivated by their inherent bidirectional architecture and recent success in matching or surpassing LLMs especially on reasoning tasks. We present the first systematic study of the diffusion language embedding model, which outperforms the LLM-based embedding model by 20% on long-document retrieval, 8% on reasoning-intensive retrieval, 2% on instruction-following retrieval, and achieve competitive performance on traditional text embedding benchmarks. Our analysis verifies that bidirectional attention is crucial for encoding global context in long and complex text.

Accelerating large language model (LLM) inference is critical for real-world deployments requiring high throughput and low latency. Contextual sparsity, where each token dynamically activates only a small subset of the model parameters, shows promise but does not scale to large batch sizes due to union of active neurons quickly approaching dense computation. We introduce Polar Sparsity, highlighting a key shift in sparsity importance from MLP to Attention layers as we scale batch size and sequence length. While MLP layers become more compute-efficient under batching, their sparsity vanishes. In contrast, attention becomes increasingly more expensive at scale, while their head sparsity remains stable and batch-invariant. We develop hardware-efficient, sparsity-aware GPU kernels for selective MLP and Attention computations, delivering up to \(2.2\times\) end-to-end speedups for models like OPT, LLaMA-2 \& 3, across various batch sizes and sequence lengths without compromising accuracy. To our knowledge, this is the first work to demonstrate that contextual sparsity can scale effectively to large batch sizes, delivering substantial inference acceleration with minimal changes, making Polar Sparsity practical for large-scale, high-throughput LLM deployment systems. Our code is available at: https://github.com/susavlsh10/Polar-Sparsity.

The Muon optimizer is consistently faster than Adam in training Large Language Models (LLMs), yet the mechanism underlying its success remains unclear. This paper demystifies this mechanism through the lens of associative memory. By ablating the transformer components optimized by Muon, we reveal that the associative memory parameters of LLMs, namely the Value and Output (VO) attention weights and Feed-Forward Networks (FFNs), are the primary contributors to Muon's superiority. Motivated by this associative memory view, we then explain Muon's superiority on real-world corpora, which are intrinsically heavy-tailed: a few classes (tail classes) appear far less frequently than others. The superiority is explained through two key properties: (i) its update rule consistently yields a more isotropic singular spectrum than Adam; and as a result, (ii) on heavy-tailed data, it optimizes tail classes more effectively than Adam. Beyond empirical evidence, we theoretically confirm these findings by analyzing a one-layer associative memory model under class-imbalanced data. We prove that Muon consistently achieves balanced learning across classes regardless of feature embeddings, whereas Adam can induce large disparities in learning errors depending on embedding properties. In summary, our empirical observations and theoretical analyses reveal Muon's core advantage: its update rule aligns with the outer-product structure of linear associative memories, enabling more balanced and effective learning of tail classes in heavy-tailed distributions than Adam.

Large language models (LLMs) have complicated internal dynamics, but induce representations of words and phrases whose geometry we can study. Human language processing is also opaque, but neural response measurements can provide (noisy) recordings of activation during listening or reading, from which we can extract similar representations of words and phrases. Here we study the extent to which the geometries induced by these representations, share similarities in the context of brain decoding. We find that the larger neural language models get, the more their representations are structurally similar to neural response measurements from brain imaging. Code is available at https://github.com/coastalcph/brainlm.

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - DeepProbLog, Scallop, and DomiKnowS. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

This paper introduces an efficient and robust method for discovering interpretable circuits in large language models using discrete sparse autoencoders. Our approach addresses key limitations of existing techniques, namely computational complexity and sensitivity to hyperparameters. We propose training sparse autoencoders on carefully designed positive and negative examples, where the model can only correctly predict the next token for the positive examples. We hypothesise that learned representations of attention head outputs will signal when a head is engaged in specific computations. By discretising the learned representations into integer codes and measuring the overlap between codes unique to positive examples for each head, we enable direct identification of attention heads involved in circuits without the need for expensive ablations or architectural modifications. On three well-studied tasks - indirect object identification, greater-than comparisons, and docstring completion - the proposed method achieves higher precision and recall in recovering ground-truth circuits compared to state-of-the-art baselines, while reducing runtime from hours to seconds. Notably, we require only 5-10 text examples for each task to learn robust representations. Our findings highlight the promise of discrete sparse autoencoders for scalable and efficient mechanistic interpretability, offering a new direction for analysing the inner workings of large language models.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.