Daily Papers

Domain adaptive semantic segmentation aims to transfer knowledge from a labeled source domain to an unlabeled target domain. However, existing methods primarily focus on directly learning qualified target features, making it challenging to guarantee their discrimination in the absence of target labels. This work provides a new perspective. We observe that the features learned with source data manage to keep categorically discriminative during training, thereby enabling us to implicitly learn adequate target representations by simply pulling target features close to source features for each category. To this end, we propose T2S-DA, which we interpret as a form of pulling Target to Source for Domain Adaptation, encouraging the model in learning similar cross-domain features. Also, considering the pixel categories are heavily imbalanced for segmentation datasets, we come up with a dynamic re-weighting strategy to help the model concentrate on those underperforming classes. Extensive experiments confirm that T2S-DA learns a more discriminative and generalizable representation, significantly surpassing the state-of-the-art. We further show that our method is quite qualified for the domain generalization task, verifying its domain-invariant property.

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.

Face anti-spoofing (FAS) aims at distinguishing face spoof attacks from the authentic ones, which is typically approached by learning proper models for performing the associated classification task. In practice, one would expect such models to be generalized to FAS in different image domains. Moreover, it is not practical to assume that the type of spoof attacks would be known in advance. In this paper, we propose a deep learning model for addressing the aforementioned domain-generalized face anti-spoofing task. In particular, our proposed network is able to disentangle facial liveness representation from the irrelevant ones (i.e., facial content and image domain features). The resulting liveness representation exhibits sufficient domain invariant properties, and thus it can be applied for performing domain-generalized FAS. In our experiments, we conduct experiments on five benchmark datasets with various settings, and we verify that our model performs favorably against state-of-the-art approaches in identifying novel types of spoof attacks in unseen image domains.

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder varphi^* that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder Phi^*_tau. We prove that non-commutativity steers the optimization towards Phi^*_tau instead of varphi^*, bringing the H-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning Phi^*_tau, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over 2%, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which recently received a lot of attention is described by the notion of invariance. In this work we provide a causal perspective and new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization, where we are able to significantly boost the score of existing models.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

This work studies the generalization issue of face anti-spoofing (FAS) models on domain gaps, such as image resolution, blurriness and sensor variations. Most prior works regard domain-specific signals as a negative impact, and apply metric learning or adversarial losses to remove them from feature representation. Though learning a domain-invariant feature space is viable for the training data, we show that the feature shift still exists in an unseen test domain, which backfires on the generalizability of the classifier. In this work, instead of constructing a domain-invariant feature space, we encourage domain separability while aligning the live-to-spoof transition (i.e., the trajectory from live to spoof) to be the same for all domains. We formulate this FAS strategy of separability and alignment (SA-FAS) as a problem of invariant risk minimization (IRM), and learn domain-variant feature representation but domain-invariant classifier. We demonstrate the effectiveness of SA-FAS on challenging cross-domain FAS datasets and establish state-of-the-art performance.

Distribution shift presents a significant challenge in machine learning, where models often underperform during the test stage when faced with a different distribution than the one they were trained on. This paper focuses on domain shifts, which occur when the model is applied to new domains that are different from the ones it was trained on, and propose a new approach called D^3G. Unlike previous methods that aim to learn a single model that is domain invariant, D^3G leverages domain similarities based on domain metadata to learn domain-specific models. Concretely, D^3G learns a set of training-domain-specific functions during the training stage and reweights them based on domain relations during the test stage. These domain relations can be directly obtained and learned from domain metadata. Under mild assumptions, we theoretically prove that using domain relations to reweight training-domain-specific functions achieves stronger out-of-domain generalization compared to the conventional averaging approach. Empirically, we evaluate the effectiveness of D^3G using real-world datasets for tasks such as temperature regression, land use classification, and molecule-protein binding affinity prediction. Our results show that D^3G consistently outperforms state-of-the-art methods.

Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains. However, we argue that the domain variantions also contain useful information, ie, classification-aware information, for downstream tasks, which has been largely ignored. Different from learning domain invariant features from source domains, we decouple the input images into Domain Expert Features and noise. The proposed domain expert features lie in a learned latent space where the images in each domain can be classified independently, enabling the implicit use of classification-aware domain variations. Based on the analysis, we proposed a novel paradigm called Domain Disentanglement Network (DDN) to disentangle the domain expert features from the source domain images and aggregate the source domain expert features for representing the target test domain. We also propound a new contrastive learning method to guide the domain expert features to form a more balanced and separable feature space. Experiments on the widely-used benchmarks of PACS, VLCS, OfficeHome, DomainNet, and TerraIncognita demonstrate the competitive performance of our method compared to the recently proposed alternatives.

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

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.

Domain Generalization (DG) is a challenging task in machine learning that requires a coherent ability to comprehend shifts across various domains through extraction of domain-invariant features. DG performance is typically evaluated by performing image classification in domains of various image styles. However, current methodology lacks quantitative understanding about shifts in stylistic domain, and relies on a vast amount of pre-training data, such as ImageNet1K, which are predominantly in photo-realistic style with weakly supervised class labels. Such a data-driven practice could potentially result in spurious correlation and inflated performance on DG benchmarks. In this paper, we introduce a new DG paradigm to address these risks. We first introduce two new quantitative measures ICV and IDD to describe domain shifts in terms of consistency of classes within one domain and similarity between two stylistic domains. We then present SuperMarioDomains (SMD), a novel synthetic multi-domain dataset sampled from video game scenes with more consistent classes and sufficient dissimilarity compared to ImageNet1K. We demonstrate our DG method SMOS. SMOS first uses SMD to train a precursor model, which is then used to ground the training on a DG benchmark. We observe that SMOS contributes to state-of-the-art performance across five DG benchmarks, gaining large improvements to performances on abstract domains along with on-par or slight improvements to those on photo-realistic domains. Our qualitative analysis suggests that these improvements can be attributed to reduced distributional divergence between originally distant domains. Our data are available at https://github.com/fpsluozi/SMD-SMOS .

This paper investigates discrepancies in how neural networks learn from different imaging domains, which are commonly overlooked when adopting computer vision techniques from the domain of natural images to other specialized domains such as medical images. Recent works have found that the generalization error of a trained network typically increases with the intrinsic dimension (d_{data}) of its training set. Yet, the steepness of this relationship varies significantly between medical (radiological) and natural imaging domains, with no existing theoretical explanation. We address this gap in knowledge by establishing and empirically validating a generalization scaling law with respect to d_{data}, and propose that the substantial scaling discrepancy between the two considered domains may be at least partially attributed to the higher intrinsic ``label sharpness'' (K_F) of medical imaging datasets, a metric which we propose. Next, we demonstrate an additional benefit of measuring the label sharpness of a training set: it is negatively correlated with the trained model's adversarial robustness, which notably leads to models for medical images having a substantially higher vulnerability to adversarial attack. Finally, we extend our d_{data} formalism to the related metric of learned representation intrinsic dimension (d_{repr}), derive a generalization scaling law with respect to d_{repr}, and show that d_{data} serves as an upper bound for d_{repr}. Our theoretical results are supported by thorough experiments with six models and eleven natural and medical imaging datasets over a range of training set sizes. Our findings offer insights into the influence of intrinsic dataset properties on generalization, representation learning, and robustness in deep neural networks. Code link: https://github.com/mazurowski-lab/intrinsic-properties

The phenomenon of adversarial examples illustrates one of the most basic vulnerabilities of deep neural networks. Among the variety of techniques introduced to surmount this inherent weakness, adversarial training has emerged as the most effective strategy for learning robust models. Typically, this is achieved by balancing robust and natural objectives. In this work, we aim to further optimize the trade-off between robust and standard accuracy by enforcing a domain-invariant feature representation. We present a new adversarial training method, Domain Invariant Adversarial Learning (DIAL), which learns a feature representation that is both robust and domain invariant. DIAL uses a variant of Domain Adversarial Neural Network (DANN) on the natural domain and its corresponding adversarial domain. In the case where the source domain consists of natural examples and the target domain is the adversarially perturbed examples, our method learns a feature representation constrained not to discriminate between the natural and adversarial examples, and can therefore achieve a more robust representation. DIAL is a generic and modular technique that can be easily incorporated into any adversarial training method. Our experiments indicate that incorporating DIAL in the adversarial training process improves both robustness and standard accuracy.

We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model that will best generalize to an unseen target domain. As such, many prior approaches focus on learning representations which persist across all source domains with the assumption that these domain agnostic representations will generalize well. However, often individual domains contain characteristics which are unique and when leveraged can significantly aid in-domain recognition performance. To produce a model which best generalizes to both seen and unseen domains, we propose learning domain specific masks. The masks are encouraged to learn a balance of domain-invariant and domain-specific features, thus enabling a model which can benefit from the predictive power of specialized features while retaining the universal applicability of domain-invariant features. We demonstrate competitive performance compared to naive baselines and state-of-the-art methods on both PACS and DomainNet.

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.

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in domain-adversarial training as a local Nash equilibrium, we show that gradient descent in domain-adversarial training can violate the asymptotic convergence guarantees of the optimizer, oftentimes hindering the transfer performance. Our analysis leads us to replace gradient descent with high-order ODE solvers (i.e., Runge-Kutta), for which we derive asymptotic convergence guarantees. This family of optimizers is significantly more stable and allows more aggressive learning rates, leading to high performance gains when used as a drop-in replacement over standard optimizers. Our experiments show that in conjunction with state-of-the-art domain-adversarial methods, we achieve up to 3.5% improvement with less than of half training iterations. Our optimizers are easy to implement, free of additional parameters, and can be plugged into any domain-adversarial framework.

Unsupervised domain translation (UDT) aims to find functions that convert samples from one domain (e.g., sketches) to another domain (e.g., photos) without changing the high-level semantic meaning (also referred to as ``content''). The translation functions are often sought by probability distribution matching of the transformed source domain and target domain. CycleGAN stands as arguably the most representative approach among this line of work. However, it was noticed in the literature that CycleGAN and variants could fail to identify the desired translation functions and produce content-misaligned translations. This limitation arises due to the presence of multiple translation functions -- referred to as ``measure-preserving automorphism" (MPA) -- in the solution space of the learning criteria. Despite awareness of such identifiability issues, solutions have remained elusive. This study delves into the core identifiability inquiry and introduces an MPA elimination theory. Our analysis shows that MPA is unlikely to exist, if multiple pairs of diverse cross-domain conditional distributions are matched by the learning function. Our theory leads to a UDT learner using distribution matching over auxiliary variable-induced subsets of the domains -- other than over the entire data domains as in the classical approaches. The proposed framework is the first to rigorously establish translation identifiability under reasonable UDT settings, to our best knowledge. Experiments corroborate with our theoretical claims.

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

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at https://github.com/liangchen527/RIDG.

Recent domain generalization (DG) approaches typically use the hypothesis learned on source domains for inference on the unseen target domain. However, such a hypothesis can be arbitrarily far from the optimal one for the target domain, induced by a gap termed ``adaptivity gap''. Without exploiting the domain information from the unseen test samples, adaptivity gap estimation and minimization are intractable, which hinders us to robustify a model to any unknown distribution. In this paper, we first establish a generalization bound that explicitly considers the adaptivity gap. Our bound motivates two strategies to reduce the gap: the first one is ensembling multiple classifiers to enrich the hypothesis space, then we propose effective gap estimation methods for guiding the selection of a better hypothesis for the target. The other method is minimizing the gap directly by adapting model parameters using online target samples. We thus propose Domain-specific Risk Minimization (DRM). During training, DRM models the distributions of different source domains separately; for inference, DRM performs online model steering using the source hypothesis for each arriving target sample. Extensive experiments demonstrate the effectiveness of the proposed DRM for domain generalization with the following advantages: 1) it significantly outperforms competitive baselines on different distributional shift settings; 2) it achieves either comparable or superior accuracies on all source domains compared to vanilla empirical risk minimization; 3) it remains simple and efficient during training, and 4) it is complementary to invariant learning approaches.

Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, "dormant" directions, which do not affect the output. This provides an opportunity: By "repurposing" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one "expanded" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains. Code and project page available at https://yotamnitzan.github.io/domain-expansion/.

Medical imaging datasets often vary due to differences in acquisition protocols, patient demographics, and imaging devices. These variations in data distribution, known as domain shift, present a significant challenge in adapting imaging analysis models for practical healthcare applications. Most current domain adaptation (DA) approaches aim either to align the distributions between the source and target domains or to learn an invariant feature space that generalizes well across all domains. However, both strategies require access to a sufficient number of examples, though not necessarily annotated, from the test domain during training. This limitation hinders the widespread deployment of models in clinical settings, where target domain data may only be accessible in real time. In this work, we introduce HyDA, a novel hypernetwork framework that leverages domain characteristics rather than suppressing them, enabling dynamic adaptation at inference time. Specifically, HyDA learns implicit domain representations and uses them to adjust model parameters on-the-fly, effectively interpolating to unseen domains. We validate HyDA on two clinically relevant applications - MRI brain age prediction and chest X-ray pathology classification - demonstrating its ability to generalize across tasks and modalities. Our code is available at TBD.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Transfer learning is a powerful technique for knowledge-sharing between different tasks. Recent work has found that the representations of models with certain invariances, such as to adversarial input perturbations, achieve higher performance on downstream tasks. These findings suggest that invariance may be an important property in the context of transfer learning. However, the relationship of invariance with transfer performance is not fully understood yet and a number of questions remain. For instance, how important is invariance compared to other factors of the pretraining task? How transferable is learned invariance? In this work, we systematically investigate the importance of representational invariance for transfer learning, as well as how it interacts with other parameters during pretraining. To do so, we introduce a family of synthetic datasets that allow us to precisely control factors of variation both in training and test data. Using these datasets, we a) show that for learning representations with high transfer performance, invariance to the right transformations is as, or often more, important than most other factors such as the number of training samples, the model architecture and the identity of the pretraining classes, b) show conditions under which invariance can harm the ability to transfer representations and c) explore how transferable invariance is between tasks. The code is available at https://github.com/tillspeicher/representation-invariance-transfer.

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG). We relax this non-trivial constrained optimization problem to a tractable form with finite-dimensional parameterization and empirical approximation. Then a theoretical analysis of the extent to which the above transformations deviates from the original problem is provided. Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization. In contrast to traditional approaches based on domain adversarial training and domain labels, DDG jointly learns semantic and variation encoders for disentanglement, enabling flexible manipulation and augmentation on training data. DDG aims to learn intrinsic representations of semantic concepts that are invariant to nuisance factors and generalizable across domains. Comprehensive experiments on popular benchmarks show that DDG can achieve competitive OOD performance and uncover interpretable salient structures within data.

Existing person re-identification models often have low generalizability, which is mostly due to limited availability of large-scale labeled data in training. However, labeling large-scale training data is very expensive and time-consuming, while large-scale synthetic dataset shows promising value in learning generalizable person re-identification models. Therefore, in this paper a novel and practical person re-identification task is proposed,i.e. how to use labeled synthetic dataset and unlabeled real-world dataset to train a universal model. In this way, human annotations are no longer required, and it is scalable to large and diverse real-world datasets. To address the task, we introduce a framework with high generalizability, namely DomainMix. Specifically, the proposed method firstly clusters the unlabeled real-world images and selects the reliable clusters. During training, to address the large domain gap between two domains, a domain-invariant feature learning method is proposed, which introduces a new loss,i.e. domain balance loss, to conduct an adversarial learning between domain-invariant feature learning and domain discrimination, and meanwhile learns a discriminative feature for person re-identification. This way, the domain gap between synthetic and real-world data is much reduced, and the learned feature is generalizable thanks to the large-scale and diverse training data. Experimental results show that the proposed annotation-free method is more or less comparable to the counterpart trained with full human annotations, which is quite promising. In addition, it achieves the current state of the art on several person re-identification datasets under direct cross-dataset evaluation.

Domain adaptive detection aims to improve the generality of a detector, learned from the labeled source domain, on the unlabeled target domain. In this work, drawing inspiration from the concept of stability from the control theory that a robust system requires to remain consistent both externally and internally regardless of disturbances, we propose a novel framework that achieves unsupervised domain adaptive detection through stability analysis. In specific, we treat discrepancies between images and regions from different domains as disturbances, and introduce a novel simple but effective Network Stability Analysis (NSA) framework that considers various disturbances for domain adaptation. Particularly, we explore three types of perturbations including heavy and light image-level disturbances and instancelevel disturbance. For each type, NSA performs external consistency analysis on the outputs from raw and perturbed images and/or internal consistency analysis on their features, using teacher-student models. By integrating NSA into Faster R-CNN, we immediately achieve state-of-the-art results. In particular, we set a new record of 52.7% mAP on Cityscapes-to-FoggyCityscapes, showing the potential of NSA for domain adaptive detection. It is worth noticing, our NSA is designed for general purpose, and thus applicable to one-stage detection model (e.g., FCOS) besides the adopted one, as shown by experiments. https://github.com/tiankongzhang/NSA.

LiDAR-based 3D detectors need large datasets for training, yet they struggle to generalize to novel domains. Domain Generalization (DG) aims to mitigate this by training detectors that are invariant to such domain shifts. Current DG approaches exclusively rely on global geometric features (point cloud Cartesian coordinates) as input features. Over-reliance on these global geometric features can, however, cause 3D detectors to prioritize object location and absolute position, resulting in poor cross-domain performance. To mitigate this, we propose to exploit explicit local point cloud structure for DG, in particular by encoding point cloud neighborhoods with Gaussian blobs, GBlobs. Our proposed formulation is highly efficient and requires no additional parameters. Without any bells and whistles, simply by integrating GBlobs in existing detectors, we beat the current state-of-the-art in challenging single-source DG benchmarks by over 21 mAP (Waymo->KITTI), 13 mAP (KITTI->Waymo), and 12 mAP (nuScenes->KITTI), without sacrificing in-domain performance. Additionally, GBlobs demonstrate exceptional performance in multi-source DG, surpassing the current state-of-the-art by 17, 12, and 5 mAP on Waymo, KITTI, and ONCE, respectively.

Property prediction accuracy has long been a key parameter of machine learning in materials informatics. Accordingly, advanced models showing state-of-the-art performance turn into highly parameterized black boxes missing interpretability. Here, we present an elegant way to make their reasoning transparent. Human-readable text-based descriptions automatically generated within a suite of open-source tools are proposed as materials representation. Transformer language models pretrained on 2 million peer-reviewed articles take as input well-known terms, e.g., chemical composition, crystal symmetry, and site geometry. Our approach outperforms crystal graph networks by classifying four out of five analyzed properties if one considers all available reference data. Moreover, fine-tuned text-based models show high accuracy in the ultra-small data limit. Explanations of their internal machinery are produced using local interpretability techniques and are faithful and consistent with domain expert rationales. This language-centric framework makes accurate property predictions accessible to people without artificial-intelligence expertise.

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, a popular framework for unsupervised domain adaptation (UDA) is domain matching, in which algorithms try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, is limited and existing theoretical results are not precise enough to characterize their performance in practice. In this paper, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bounds include a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.

The objective of domain generalization (DG) is to enhance the transferability of the model learned from a source domain to unobserved domains. To prevent overfitting to a specific domain, Sharpness-Aware Minimization (SAM) reduces source domain's loss sharpness. Although SAM variants have delivered significant improvements in DG, we highlight that there's still potential for improvement in generalizing to unknown domains through the exploration on data space. This paper introduces an objective rooted in both parameter and data perturbed regions for domain generalization, coined Unknown Domain Inconsistency Minimization (UDIM). UDIM reduces the loss landscape inconsistency between source domain and unknown domains. As unknown domains are inaccessible, these domains are empirically crafted by perturbing instances from the source domain dataset. In particular, by aligning the loss landscape acquired in the source domain to the loss landscape of perturbed domains, we expect to achieve generalization grounded on these flat minima for the unknown domains. Theoretically, we validate that merging SAM optimization with the UDIM objective establishes an upper bound for the true objective of the DG task. In an empirical aspect, UDIM consistently outperforms SAM variants across multiple DG benchmark datasets. Notably, UDIM shows statistically significant improvements in scenarios with more restrictive domain information, underscoring UDIM's generalization capability in unseen domains. Our code is available at https://github.com/SJShin-AI/UDIM.

Domain generalization (DG) is a principal task to evaluate the robustness of computer vision models. Many previous studies have used normalization for DG. In normalization, statistics and normalized features are regarded as style and content, respectively. However, it has a content variation problem when removing style because the boundary between content and style is unclear. This study addresses this problem from the frequency domain perspective, where amplitude and phase are considered as style and content, respectively. First, we verify the quantitative phase variation of normalization through the mathematical derivation of the Fourier transform formula. Then, based on this, we propose a novel normalization method, PCNorm, which eliminates style only as the preserving content through spectral decomposition. Furthermore, we propose advanced PCNorm variants, CCNorm and SCNorm, which adjust the degrees of variations in content and style, respectively. Thus, they can learn domain-agnostic representations for DG. With the normalization methods, we propose ResNet-variant models, DAC-P and DAC-SC, which are robust to the domain gap. The proposed models outperform other recent DG methods. The DAC-SC achieves an average state-of-the-art performance of 65.6% on five datasets: PACS, VLCS, Office-Home, DomainNet, and TerraIncognita.

Unsupervised domain adaptation (UDA) refers to a domain adaptation framework in which a learning model is trained based on the labeled samples on the source domain and unlabelled ones in the target domain. The dominant existing methods in the field that rely on the classical covariate shift assumption to learn domain-invariant feature representation have yielded suboptimal performance under the label distribution shift between source and target domains. In this paper, we propose a novel conditional adversarial support alignment (CASA) whose aim is to minimize the conditional symmetric support divergence between the source's and target domain's feature representation distributions, aiming at a more helpful representation for the classification task. We also introduce a novel theoretical target risk bound, which justifies the merits of aligning the supports of conditional feature distributions compared to the existing marginal support alignment approach in the UDA settings. We then provide a complete training process for learning in which the objective optimization functions are precisely based on the proposed target risk bound. Our empirical results demonstrate that CASA outperforms other state-of-the-art methods on different UDA benchmark tasks under label shift conditions.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

Face anti-spoofing (FAS) based on domain generalization (DG) has been recently studied to improve the generalization on unseen scenarios. Previous methods typically rely on domain labels to align the distribution of each domain for learning domain-invariant representations. However, artificial domain labels are coarse-grained and subjective, which cannot reflect real domain distributions accurately. Besides, such domain-aware methods focus on domain-level alignment, which is not fine-grained enough to ensure that learned representations are insensitive to domain styles. To address these issues, we propose a novel perspective for DG FAS that aligns features on the instance level without the need for domain labels. Specifically, Instance-Aware Domain Generalization framework is proposed to learn the generalizable feature by weakening the features' sensitivity to instance-specific styles. Concretely, we propose Asymmetric Instance Adaptive Whitening to adaptively eliminate the style-sensitive feature correlation, boosting the generalization. Moreover, Dynamic Kernel Generator and Categorical Style Assembly are proposed to first extract the instance-specific features and then generate the style-diversified features with large style shifts, respectively, further facilitating the learning of style-insensitive features. Extensive experiments and analysis demonstrate the superiority of our method over state-of-the-art competitors. Code will be publicly available at https://github.com/qianyuzqy/IADG.

We analyze various consequences in relation to the extension of operators T:Xto Y that are p-compact, as well as the extension of operators T:Xto Y whose adjoints T^*:Y^*to X^* are p-compact. In most cases, we discuss these extension properties when the underlying spaces, either domain or codomain, are P_lambda spaces. We also answer if these extensions are almost norm-preserving in such circumstances where the extension T of a T exists. It is observed that an operator can often be extended to a larger domain when the codomain is appropriately extended as well. Specific assumptions might enable us to obtain an extension of an operator that maintains the same range. Necessary and sufficient conditions are derived for a Banach space to be L_1-predual.

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

Adapting standard methods from geometric measure theory, we provide an example of a polynomial-valued measure mu on tame sets in R^d which satisfies many desirable properties. Among these is strict monotonicity: the measure of a proper subset is strictly less than the measure of the whole set. Using techniques from non-standard analysis, we display that the domain of mu can be extended to all subsets of R^d (up to equivalence modulo infinitesimals). The resulting extension is a numerosity function that encodes the i-dimensional Hausdorff measure for all iin N, as well as the i-th intrinsic volume functions.

In domain generalization (DG), the target domain is unknown when the model is being trained, and the trained model should successfully work on an arbitrary (and possibly unseen) target domain during inference. This is a difficult problem, and despite active studies in recent years, it remains a great challenge. In this paper, we take a simple yet effective approach to tackle this issue. We propose test-time style shifting, which shifts the style of the test sample (that has a large style gap with the source domains) to the nearest source domain that the model is already familiar with, before making the prediction. This strategy enables the model to handle any target domains with arbitrary style statistics, without additional model update at test-time. Additionally, we propose style balancing, which provides a great platform for maximizing the advantage of test-time style shifting by handling the DG-specific imbalance issues. The proposed ideas are easy to implement and successfully work in conjunction with various other DG schemes. Experimental results on different datasets show the effectiveness of our methods.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

Domain generalization (DG) aims to learn a robust model from source domains that generalize well on unseen target domains. Recent studies focus on generating novel domain samples or features to diversify distributions complementary to source domains. Yet, these approaches can hardly deal with the restriction that the samples synthesized from various domains can cause semantic distortion. In this paper, we propose an online one-stage Cross Contrasting Feature Perturbation (CCFP) framework to simulate domain shift by generating perturbed features in the latent space while regularizing the model prediction against domain shift. Different from the previous fixed synthesizing strategy, we design modules with learnable feature perturbations and semantic consistency constraints. In contrast to prior work, our method does not use any generative-based models or domain labels. We conduct extensive experiments on a standard DomainBed benchmark with a strict evaluation protocol for a fair comparison. Comprehensive experiments show that our method outperforms the previous state-of-the-art, and quantitative analyses illustrate that our approach can alleviate the domain shift problem in out-of-distribution (OOD) scenarios.

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

Let mathbb H be the finite direct sums of H^2(mathbb D). In this paper, we give a characterization of the closed subspaces of mathbb H which are invariant under the shift, thus obtaining a concrete Beurling-type theorem for the finite index shift. This characterization presents any such a subspace as the finite intersection, up to an inner function, of pre-images of a closed shift-invariant subspace of H^2(mathbb D) under ``determinantal operators'' from mathbb H to H^2(mathbb D), that is, continuous linear operators which intertwine the shifts and appear as determinants of matrices with entries given by bounded holomorphic functions. With simple algebraic manipulations we provide a direct proof that every invariant closed subspace of codimension at least two sits into a non-trivial closed invariant subspace. As a consequence every bounded linear operator with finite defect has a nontrivial closed invariant subspace.

Given appropriate representations of the semantic relations between carpenter and wood and between mason and stone (for example, vectors in a vector space model), a suitable algorithm should be able to recognize that these relations are highly similar (carpenter is to wood as mason is to stone; the relations are analogous). Likewise, with representations of dog, house, and kennel, an algorithm should be able to recognize that the semantic composition of dog and house, dog house, is highly similar to kennel (dog house and kennel are synonymous). It seems that these two tasks, recognizing relations and compositions, are closely connected. However, up to now, the best models for relations are significantly different from the best models for compositions. In this paper, we introduce a dual-space model that unifies these two tasks. This model matches the performance of the best previous models for relations and compositions. The dual-space model consists of a space for measuring domain similarity and a space for measuring function similarity. Carpenter and wood share the same domain, the domain of carpentry. Mason and stone share the same domain, the domain of masonry. Carpenter and mason share the same function, the function of artisans. Wood and stone share the same function, the function of materials. In the composition dog house, kennel has some domain overlap with both dog and house (the domains of pets and buildings). The function of kennel is similar to the function of house (the function of shelters). By combining domain and function similarities in various ways, we can model relations, compositions, and other aspects of semantics.

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

Recent studies on face forgery detection have shown satisfactory performance for methods involved in training datasets, but are not ideal enough for unknown domains. This motivates many works to improve the generalization, but forgery-irrelevant information, such as image background and identity, still exists in different domain features and causes unexpected clustering, limiting the generalization. In this paper, we propose a controllable guide-space (GS) method to enhance the discrimination of different forgery domains, so as to increase the forgery relevance of features and thereby improve the generalization. The well-designed guide-space can simultaneously achieve both the proper separation of forgery domains and the large distance between real-forgery domains in an explicit and controllable manner. Moreover, for better discrimination, we use a decoupling module to weaken the interference of forgery-irrelevant correlations between domains. Furthermore, we make adjustments to the decision boundary manifold according to the clustering degree of the same domain features within the neighborhood. Extensive experiments in multiple in-domain and cross-domain settings confirm that our method can achieve state-of-the-art generalization.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

Feature Selection (FS) under domain adaptation (DA) is a critical task in machine learning, especially when dealing with limited target data. However, existing methods lack the capability to guarantee the reliability of FS under DA. In this paper, we introduce a novel statistical method to statistically test FS reliability under DA, named SFS-DA (statistical FS-DA). The key strength of SFS-DA lies in its ability to control the false positive rate (FPR) below a pre-specified level alpha (e.g., 0.05) while maximizing the true positive rate. Compared to the literature on statistical FS, SFS-DA presents a unique challenge in addressing the effect of DA to ensure the validity of the inference on FS results. We overcome this challenge by leveraging the Selective Inference (SI) framework. Specifically, by carefully examining the FS process under DA whose operations can be characterized by linear and quadratic inequalities, we prove that achieving FPR control in SFS-DA is indeed possible. Furthermore, we enhance the true detection rate by introducing a more strategic approach. Experiments conducted on both synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed SFS-DA method.

Recognizing the prevalence of domain shift as a common challenge in machine learning, various domain generalization (DG) techniques have been developed to enhance the performance of machine learning systems when dealing with out-of-distribution (OOD) data. Furthermore, in real-world scenarios, data distributions can gradually change across a sequence of sequential domains. While current methodologies primarily focus on improving model effectiveness within these new domains, they often overlook fairness issues throughout the learning process. In response, we introduce an innovative framework called Counterfactual Fairness-Aware Domain Generalization with Sequential Autoencoder (CDSAE). This approach effectively separates environmental information and sensitive attributes from the embedded representation of classification features. This concurrent separation not only greatly improves model generalization across diverse and unfamiliar domains but also effectively addresses challenges related to unfair classification. Our strategy is rooted in the principles of causal inference to tackle these dual issues. To examine the intricate relationship between semantic information, sensitive attributes, and environmental cues, we systematically categorize exogenous uncertainty factors into four latent variables: 1) semantic information influenced by sensitive attributes, 2) semantic information unaffected by sensitive attributes, 3) environmental cues influenced by sensitive attributes, and 4) environmental cues unaffected by sensitive attributes. By incorporating fairness regularization, we exclusively employ semantic information for classification purposes. Empirical validation on synthetic and real-world datasets substantiates the effectiveness of our approach, demonstrating improved accuracy levels while ensuring the preservation of fairness in the evolving landscape of continuous domains.

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

Molecule generation is advancing rapidly in chemical discovery and drug design. Flow matching methods have recently set the state of the art (SOTA) in unconditional molecule generation, surpassing score-based diffusion models. However, diffusion models still lead in property-guided generation. In this work, we introduce PropMolFlow, a novel approach for property-guided molecule generation based on geometry-complete SE(3)-equivariant flow matching. Integrating five different property embedding methods with a Gaussian expansion of scalar properties, PropMolFlow outperforms previous SOTA diffusion models in conditional molecule generation across various properties while preserving the stability and validity of the generated molecules, consistent with its unconditional counterpart. Additionally, it enables faster inference with significantly fewer time steps compared to baseline models. We highlight the importance of validating the properties of generated molecules through DFT calculations performed at the same level of theory as the training data. Specifically, our analysis identifies properties that require DFT validation and others where a pretrained SE(3) geometric vector perceptron regressors provide sufficiently accurate predictions on generated molecules. Furthermore, we introduce a new property metric designed to assess the model's ability to propose molecules with underrepresented property values, assessing its capacity for out-of-distribution generalization. Our findings reveal shortcomings in existing structural metrics, which mistakenly validate open-shell molecules or molecules with invalid valence-charge configurations, underscoring the need for improved evaluation frameworks. Overall, this work paves the way for developing targeted property-guided generation methods, enhancing the design of molecular generative models for diverse applications.

Domain Generalization aims to develop models that can generalize to novel and unseen data distributions. In this work, we study how model architectures and pre-training objectives impact feature richness and propose a method to effectively leverage them for domain generalization. Specifically, given a pre-trained feature space, we first discover latent domain structures, referred to as pseudo-domains, that capture domain-specific variations in an unsupervised manner. Next, we augment existing classifiers with these complementary pseudo-domain representations making them more amenable to diverse unseen test domains. We analyze how different pre-training feature spaces differ in the domain-specific variances they capture. Our empirical studies reveal that features from diffusion models excel at separating domains in the absence of explicit domain labels and capture nuanced domain-specific information. On 5 datasets, we show that our very simple framework improves generalization to unseen domains by a maximum test accuracy improvement of over 4% compared to the standard baseline Empirical Risk Minimization (ERM). Crucially, our method outperforms most algorithms that access domain labels during training.

Diabetic Retinopathy (DR), induced by diabetes, poses a significant risk of visual impairment. Accurate and effective grading of DR aids in the treatment of this condition. Yet existing models experience notable performance degradation on unseen domains due to domain shifts. Previous methods address this issue by simulating domain style through simple visual transformation and mitigating domain noise via learning robust representations. However, domain shifts encompass more than image styles. They overlook biases caused by implicit factors such as ethnicity, age, and diagnostic criteria. In our work, we propose a novel framework where representations of paired data from different domains are decoupled into semantic features and domain noise. The resulting augmented representation comprises original retinal semantics and domain noise from other domains, aiming to generate enhanced representations aligned with real-world clinical needs, incorporating rich information from diverse domains. Subsequently, to improve the robustness of the decoupled representations, class and domain prototypes are employed to interpolate the disentangled representations while data-aware weights are designed to focus on rare classes and domains. Finally, we devise a robust pixel-level semantic alignment loss to align retinal semantics decoupled from features, maintaining a balance between intra-class diversity and dense class features. Experimental results on multiple benchmarks demonstrate the effectiveness of our method on unseen domains. The code implementations are accessible on https://github.com/richard-peng-xia/DECO.

Domain Generation Algorithms (DGAs) are frequently used to generate numerous domains for use by botnets. These domains are often utilized as rendezvous points for servers that malware has command and control over. There are many algorithms that are used to generate domains, however many of these algorithms are simplistic and easily detected by traditional machine learning techniques. In this paper, three variants of Generative Adversarial Networks (GANs) are optimized to generate domains which have similar characteristics of benign domains, resulting in domains which greatly evade several state-of-the-art deep learning based DGA classifiers. We additionally provide a detailed analysis into offensive usability for each variant with respect to repeated and existing domain collisions. Finally, we fine-tune the state-of-the-art DGA classifiers by adding GAN generated samples to their original training datasets and analyze the changes in performance. Our results conclude that GAN based DGAs are superior in evading DGA classifiers in comparison to traditional DGAs, and of the variants, the Wasserstein GAN with Gradient Penalty (WGANGP) is the highest performing DGA for uses both offensively and defensively.

Domain adaptation framework of GANs has achieved great progress in recent years as a main successful approach of training contemporary GANs in the case of very limited training data. In this work, we significantly improve this framework by proposing an extremely compact parameter space for fine-tuning the generator. We introduce a novel domain-modulation technique that allows to optimize only 6 thousand-dimensional vector instead of 30 million weights of StyleGAN2 to adapt to a target domain. We apply this parameterization to the state-of-art domain adaptation methods and show that it has almost the same expressiveness as the full parameter space. Additionally, we propose a new regularization loss that considerably enhances the diversity of the fine-tuned generator. Inspired by the reduction in the size of the optimizing parameter space we consider the problem of multi-domain adaptation of GANs, i.e. setting when the same model can adapt to several domains depending on the input query. We propose the HyperDomainNet that is a hypernetwork that predicts our parameterization given the target domain. We empirically confirm that it can successfully learn a number of domains at once and may even generalize to unseen domains. Source code can be found at https://github.com/MACderRu/HyperDomainNet

Domain Adaptation (DA) is a method for enhancing a model's performance on a target domain with inadequate annotated data by applying the information the model has acquired from a related source domain with sufficient labeled data. The escalating enforcement of data-privacy regulations like HIPAA, COPPA, FERPA, etc. have sparked a heightened interest in adapting models to novel domains while circumventing the need for direct access to the source data, a problem known as Source-Free Domain Adaptation (SFDA). In this paper, we propose a novel framework for SFDA that generates source data using a text-to-image diffusion model trained on the target domain samples. Our method starts by training a text-to-image diffusion model on the labeled target domain samples, which is then fine-tuned using the pre-trained source model to generate samples close to the source data. Finally, we use Domain Adaptation techniques to align the artificially generated source data with the target domain data, resulting in significant performance improvements of the model on the target domain. Through extensive comparison against several baselines on the standard Office-31, Office-Home, and VisDA benchmarks, we demonstrate the effectiveness of our approach for the SFDA task.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical systems as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement and causal factorization, we aim to separate the domain parameters from the dynamics in the latent space of generative models. In our experiments we model dynamics both in phase space and in video sequences and conduct rigorous OOD evaluations. Results indicate that disentangled VAEs adapt better to domain parameters spaces that were not present in the training data. At the same time, disentanglement can improve the long-term and out-of-distribution predictions of state-of-the-art models in video sequences.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.

Domain generalization (DG) is proposed to deal with the issue of domain shift, which occurs when statistical differences exist between source and target domains. However, most current methods do not account for a common realistic scenario where the source and target domains have different classes. To overcome this deficiency, open set domain generalization (OSDG) then emerges as a more practical setting to recognize unseen classes in unseen domains. An intuitive approach is to use multiple one-vs-all classifiers to define decision boundaries for each class and reject the outliers as unknown. However, the significant class imbalance between positive and negative samples often causes the boundaries biased towards positive ones, resulting in misclassification for known samples in the unseen target domain. In this paper, we propose a novel meta-learning-based framework called dualistic MEta-learning with joint DomaIn-Class matching (MEDIC), which considers gradient matching towards inter-domain and inter-class splits simultaneously to find a generalizable boundary balanced for all tasks. Experimental results demonstrate that MEDIC not only outperforms previous methods in open set scenarios, but also maintains competitive close set generalization ability at the same time. Our code is available at https://github.com/zzwdx/MEDIC.

In Self-Supervised Learning (SSL), models are typically pretrained, fine-tuned, and evaluated on the same domains. However, they tend to perform poorly when evaluated on unseen domains, a challenge that Unsupervised Domain Generalization (UDG) seeks to address. Current UDG methods rely on domain labels, which are often challenging to collect, and domain-specific architectures that lack scalability when confronted with numerous domains, making the current methodology impractical and rigid. Inspired by contrastive-based UDG methods that mitigate spurious correlations by restricting comparisons to examples from the same domain, we hypothesize that eliminating style variability within a batch could provide a more convenient and flexible way to reduce spurious correlations without requiring domain labels. To verify this hypothesis, we introduce Batch Styles Standardization (BSS), a relatively simple yet powerful Fourier-based method to standardize the style of images in a batch specifically designed for integration with SSL methods to tackle UDG. Combining BSS with existing SSL methods offers serious advantages over prior UDG methods: (1) It eliminates the need for domain labels or domain-specific network components to enhance domain-invariance in SSL representations, and (2) offers flexibility as BSS can be seamlessly integrated with diverse contrastive-based but also non-contrastive-based SSL methods. Experiments on several UDG datasets demonstrate that it significantly improves downstream task performances on unseen domains, often outperforming or rivaling with UDG methods. Finally, this work clarifies the underlying mechanisms contributing to BSS's effectiveness in improving domain-invariance in SSL representations and performances on unseen domain.

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

To deal with the domain shift between training and test samples, current methods have primarily focused on learning generalizable features during training and ignore the specificity of unseen samples that are also critical during the test. In this paper, we investigate a more challenging task that aims to adapt a trained CNN model to unseen domains during the test. To maximumly mine the information in the test data, we propose a unified method called DomainAdaptor for the test-time adaptation, which consists of an AdaMixBN module and a Generalized Entropy Minimization (GEM) loss. Specifically, AdaMixBN addresses the domain shift by adaptively fusing training and test statistics in the normalization layer via a dynamic mixture coefficient and a statistic transformation operation. To further enhance the adaptation ability of AdaMixBN, we design a GEM loss that extends the Entropy Minimization loss to better exploit the information in the test data. Extensive experiments show that DomainAdaptor consistently outperforms the state-of-the-art methods on four benchmarks. Furthermore, our method brings more remarkable improvement against existing methods on the few-data unseen domain. The code is available at https://github.com/koncle/DomainAdaptor.

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.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width w^*_{min}=max(d_x,d_y), where d_x and d_y are the dimensions of the input and output, respectively. Recently, cai2022achieve shows that a leaky-ReLU NN with this critical width can achieve UAP for L^p functions on a compact domain K, i.e., the UAP for L^p(K,R^{d_y}). This paper examines a uniform UAP for the function class C(K,R^{d_y}) and gives the exact minimum width of the leaky-ReLU NN as w_{min}=max(d_x+1,d_y)+1_{d_y=d_x+1}, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

In lifelong learning, an agent learns throughout its entire life without resets, in a constantly changing environment, as we humans do. Consequently, lifelong learning comes with a plethora of research problems such as continual domain shifts, which result in non-stationary rewards and environment dynamics. These non-stationarities are difficult to detect and cope with due to their continuous nature. Therefore, exploration strategies and learning methods are required that are capable of tracking the steady domain shifts, and adapting to them. We propose Reactive Exploration to track and react to continual domain shifts in lifelong reinforcement learning, and to update the policy correspondingly. To this end, we conduct experiments in order to investigate different exploration strategies. We empirically show that representatives of the policy-gradient family are better suited for lifelong learning, as they adapt more quickly to distribution shifts than Q-learning. Thereby, policy-gradient methods profit the most from Reactive Exploration and show good results in lifelong learning with continual domain shifts. Our code is available at: https://github.com/ml-jku/reactive-exploration.

Foundation models have been transformational in machine learning fields such as natural language processing and computer vision. Similar success in atomic property prediction has been limited due to the challenges of training effective models across multiple chemical domains. To address this, we introduce Joint Multi-domain Pre-training (JMP), a supervised pre-training strategy that simultaneously trains on multiple datasets from different chemical domains, treating each dataset as a unique pre-training task within a multi-task framework. Our combined training dataset consists of sim120M systems from OC20, OC22, ANI-1x, and Transition-1x. We evaluate performance and generalization by fine-tuning over a diverse set of downstream tasks and datasets including: QM9, rMD17, MatBench, QMOF, SPICE, and MD22. JMP demonstrates an average improvement of 59% over training from scratch, and matches or sets state-of-the-art on 34 out of 40 tasks. Our work highlights the potential of pre-training strategies that utilize diverse data to advance property prediction across chemical domains, especially for low-data tasks.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the Hoare hyperspace monad H, which assigns to every space its space of closed subsets equipped with the lower Vietoris topology. The second is the monad V of continuous valuations, also known as the extended probabilistic powerdomain. We construct both monads in a unified way in terms of double dualization. This reveals a close analogy between them, and allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra. Third, we show that V can be restricted to a submonad of tau-smooth probability measures on Top. By composing these two morphisms of monads, we obtain that taking the support of a tau-smooth probability measure is also a morphism of monads.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm large classes of boundary hypersurfaces are static regular. In this note, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.

We give a simple, fully correct, and assumption-light replacement for the contested "domain-extension" in Step 9 of a recent windowed-QFT lattice algorithm with complex-Gaussian windows~chen2024quantum. The published Step~9 suffers from a periodicity/support mismatch. We present a pair-shift difference construction that coherently cancels all unknown offsets, produces an exact uniform CRT-coset state over Z_{P}, and then uses the QFT to enforce the intended modular linear relation. The unitary is reversible, uses poly(log M_2) gates, and preserves the algorithm's asymptotics. Project Page: https://github.com/yifanzhang-pro/quantum-lattice.

In the field of object detection, domain generalisation (DG) aims to ensure robust performance across diverse and unseen target domains by learning the robust domain-invariant features corresponding to the objects of interest across multiple source domains. While there are many approaches established for performing DG for the task of classification, there has been a very little focus on object detection. In this paper, we propose a domain penalisation (DP) framework for the task of object detection, where the data is assumed to be sampled from multiple source domains and tested on completely unseen test domains. We assign penalisation weights to each domain, with the values updated based on the detection networks performance on the respective source domains. By prioritising the domains that needs more attention, our approach effectively balances the training process. We evaluate our solution on the GWHD 2021 dataset, a component of the WiLDS benchmark and we compare against ERM and GroupDRO as these are primarily loss function based. Our extensive experimental results reveals that the proposed approach improves the accuracy by 0.3 percent and 0.5 percent on validation and test out-of-distribution (OOD) sets, respectively for FasterRCNN. We also compare the performance of our approach on FCOS detector and show that our approach improves the baseline OOD performance over the existing approaches by 1.3 percent and 1.4 percent on validation and test sets, respectively. This study underscores the potential of performance based domain penalisation in enhancing the generalisation ability of object detection models across diverse environments.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and non-Lipschitz losses. For this setting we provide an algorithm which guarantees R_{T}(u)le tilde O(G|u|T+L|u|^{2}T) regret on any problem where the subgradients satisfy |g_{t}|le G+L|w_{t}|, and show that this bound is unimprovable without further assumptions. We leverage this algorithm to develop new saddle-point optimization algorithms that converge in duality gap in unbounded domains, even in the absence of meaningful curvature. Finally, we provide the first algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses, as well as a matching lower bound. The regret of our dynamic regret algorithm automatically improves to a novel L^{*} bound when the losses are smooth.

Despite the rapid development of machine learning algorithms for domain generalization (DG), there is no clear empirical evidence that the existing DG algorithms outperform the classic empirical risk minimization (ERM) across standard benchmarks. To better understand this phenomenon, we investigate whether there are benefits of DG algorithms over ERM through the lens of label noise. Specifically, our finite-sample analysis reveals that label noise exacerbates the effect of spurious correlations for ERM, undermining generalization. Conversely, we illustrate that DG algorithms exhibit implicit label-noise robustness during finite-sample training even when spurious correlation is present. Such desirable property helps mitigate spurious correlations and improve generalization in synthetic experiments. However, additional comprehensive experiments on real-world benchmark datasets indicate that label-noise robustness does not necessarily translate to better performance compared to ERM. We conjecture that the failure mode of ERM arising from spurious correlations may be less pronounced in practice.

It has been shown that deep neural networks of a large enough width are universal approximators but they are not if the width is too small. There were several attempts to characterize the minimum width w_{min} enabling the universal approximation property; however, only a few of them found the exact values. In this work, we show that the minimum width for L^p approximation of L^p functions from [0,1]^{d_x} to mathbb R^{d_y} is exactly max{d_x,d_y,2} if an activation function is ReLU-Like (e.g., ReLU, GELU, Softplus). Compared to the known result for ReLU networks, w_{min}=max{d_x+1,d_y} when the domain is mathbb R^{d_x}, our result first shows that approximation on a compact domain requires smaller width than on mathbb R^{d_x}. We next prove a lower bound on w_{min} for uniform approximation using general activation functions including ReLU: w_{min}ge d_y+1 if d_x<d_yle2d_x. Together with our first result, this shows a dichotomy between L^p and uniform approximations for general activation functions and input/output dimensions.

Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is pi_1-injective. Furthermore, the domain complex of groups is developable and the induced map on geometric realizations of developments is an isometric embedding.

We make two contributions in the field of AI fairness over continuous protected attributes. First, we show that the Hirschfeld-Gebelein-Renyi (HGR) indicator (the only one currently available for such a case) is valuable but subject to a few crucial limitations regarding semantics, interpretability, and robustness. Second, we introduce a family of indicators that are: 1) complementary to HGR in terms of semantics; 2) fully interpretable and transparent; 3) robust over finite samples; 4) configurable to suit specific applications. Our approach also allows us to define fine-grained constraints to permit certain types of dependence and forbid others selectively. By expanding the available options for continuous protected attributes, our approach represents a significant contribution to the area of fair artificial intelligence.

The problem of domain generalization is to learn from multiple training domains, and extract a domain-agnostic model that can then be applied to an unseen domain. Domain generalization (DG) has a clear motivation in contexts where there are target domains with distinct characteristics, yet sparse data for training. For example recognition in sketch images, which are distinctly more abstract and rarer than photos. Nevertheless, DG methods have primarily been evaluated on photo-only benchmarks focusing on alleviating the dataset bias where both problems of domain distinctiveness and data sparsity can be minimal. We argue that these benchmarks are overly straightforward, and show that simple deep learning baselines perform surprisingly well on them. In this paper, we make two main contributions: Firstly, we build upon the favorable domain shift-robust properties of deep learning methods, and develop a low-rank parameterized CNN model for end-to-end DG learning. Secondly, we develop a DG benchmark dataset covering photo, sketch, cartoon and painting domains. This is both more practically relevant, and harder (bigger domain shift) than existing benchmarks. The results show that our method outperforms existing DG alternatives, and our dataset provides a more significant DG challenge to drive future research.

Deep Neural Networks have exhibited considerable success in various visual tasks. However, when applied to unseen test datasets, state-of-the-art models often suffer performance degradation due to domain shifts. In this paper, we introduce a novel approach for domain generalization from a novel perspective of enhancing the robustness of channels in feature maps to domain shifts. We observe that models trained on source domains contain a substantial number of channels that exhibit unstable activations across different domains, which are inclined to capture domain-specific features and behave abnormally when exposed to unseen target domains. To address the issue, we propose a DomainDrop framework to continuously enhance the channel robustness to domain shifts, where a domain discriminator is used to identify and drop unstable channels in feature maps of each network layer during forward propagation. We theoretically prove that our framework could effectively lower the generalization bound. Extensive experiments on several benchmarks indicate that our framework achieves state-of-the-art performance compared to other competing methods. Our code is available at https://github.com/lingeringlight/DomainDrop.

Wireless sensing has recently found widespread applications in diverse environments, including homes, offices, and public spaces. By analyzing patterns in channel state information (CSI), it is possible to infer human actions for tasks such as person identification, gesture recognition, and fall detection. However, CSI is highly sensitive to environmental changes, where even minor alterations can significantly distort the CSI patterns. This sensitivity often leads to performance degradation or outright failure when applying wireless sensing models trained in one environment to another. To address this challenge, Domain Alignment (DAL) has been widely adopted for cross-domain classification tasks, as it focuses on aligning the global distributions of the source and target domains in feature space. Despite its popularity, DAL often neglects inter-category relationships, which can lead to misalignment between categories across domains, even when global alignment is achieved. To overcome these limitations, we propose K-Nearest Neighbors Maximum Mean Discrepancy (KNN-MMD), a novel few-shot method for cross-domain wireless sensing. Our approach begins by constructing a help set using KNN from the target domain, enabling local alignment between the source and target domains within each category using MMD. Additionally, we address a key instability issue commonly observed in cross-domain methods, where model performance fluctuates sharply between epochs. Further, most existing methods struggle to determine an optimal stopping point during training due to the absence of labeled data from the target domain. Our method resolves this by excluding the support set from the target domain during training and employing it as a validation set to determine the stopping criterion.The dataset and code are publicly available at https://github.com/RS2002/KNN-MMD .

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution, conventional feature distribution matching methods usually match the mean and standard deviation of features. However, the feature distributions of real-world data are usually much more complicated than Gaussian, which cannot be accurately matched by using only the first-order and second-order statistics, while it is computationally prohibitive to use high-order statistics for distribution matching. In this work, we, for the first time to our best knowledge, propose to perform Exact Feature Distribution Matching (EFDM) by exactly matching the empirical Cumulative Distribution Functions (eCDFs) of image features, which could be implemented by applying the Exact Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play manner with minimal cost. The effectiveness of our proposed EFDM method is verified on a variety of AST and DG tasks, demonstrating new state-of-the-art results. Codes are available at https://github.com/YBZh/EFDM.

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

Domain generalization (DG) aims to avoid the performance degradation of the model when the distribution shift between the limited training data and unseen test data occurs. Recently, foundation models with enormous parameters have been pre-trained with huge datasets, demonstrating strong generalization ability and showing promising direction for solving the DG problem. However, fully Fine-Tuning (FT) the foundation models results in unsatisfactory out-of-distribution accuracy due to the destroyed pre-trained generalized features. Recently, Parameter-Efficient Fine-Tuning (PEFT) alleviates the above problem by fine-tuning a small portion of the model parameters while keeping the rest frozen, which achieves better generalization performance compared to FT. Nevertheless, PEFT still suffers from the issue of overfitting to the training domains. To address the above issue, we propose Parameter-Efficient Group with Orthogonal regularization (PEGO) for vision transformers, which effectively preserves the generalization ability of the pre-trained network and learns more diverse knowledge compared with conventional PEFT. Specifically, we inject a group of trainable Low-Rank Adaptation (LoRA) modules into the pre-trained model and propose an orthogonal regularization loss to enhance the generalization ability of the model. Our framework achieves SOTA performance on five DG benchmarks, while only requiring training a small number of parameters without adding additional testing cost.

In this paper, we introduce analytic federated learning (AFL), a new training paradigm that brings analytical (i.e., closed-form) solutions to the federated learning (FL) community. Our AFL draws inspiration from analytic learning -- a gradient-free technique that trains neural networks with analytical solutions in one epoch. In the local client training stage, the AFL facilitates a one-epoch training, eliminating the necessity for multi-epoch updates. In the aggregation stage, we derive an absolute aggregation (AA) law. This AA law allows a single-round aggregation, removing the need for multiple aggregation rounds. More importantly, the AFL exhibits a weight-invariant property, meaning that regardless of how the full dataset is distributed among clients, the aggregated result remains identical. This could spawn various potentials, such as data heterogeneity invariance, client-number invariance, absolute convergence, and being hyperparameter-free (our AFL is the first hyperparameter-free method in FL history). We conduct experiments across various FL settings including extremely non-IID ones, and scenarios with a large number of clients (e.g., ge 1000). In all these settings, our AFL constantly performs competitively while existing FL techniques encounter various obstacles. Code is available at https://github.com/ZHUANGHP/Analytic-federated-learning

A fundamental challenge for machine learning models is how to generalize learned models for out-of-distribution (OOD) data. Among various approaches, exploiting invariant features by Domain Adversarial Training (DAT) received widespread attention. Despite its success, we observe training instability from DAT, mostly due to over-confident domain discriminator and environment label noise. To address this issue, we proposed Environment Label Smoothing (ELS), which encourages the discriminator to output soft probability, which thus reduces the confidence of the discriminator and alleviates the impact of noisy environment labels. We demonstrate, both experimentally and theoretically, that ELS can improve training stability, local convergence, and robustness to noisy environment labels. By incorporating ELS with DAT methods, we are able to yield state-of-art results on a wide range of domain generalization/adaptation tasks, particularly when the environment labels are highly noisy.

Single domain generalization aims to learn a model from a single training domain (source domain) and apply it to multiple unseen test domains (target domains). Existing methods focus on expanding the distribution of the training domain to cover the target domains, but without estimating the domain shift between the source and target domains. In this paper, we propose a new learning paradigm, namely simulate-analyze-reduce, which first simulates the domain shift by building an auxiliary domain as the target domain, then learns to analyze the causes of domain shift, and finally learns to reduce the domain shift for model adaptation. Under this paradigm, we propose a meta-causal learning method to learn meta-knowledge, that is, how to infer the causes of domain shift between the auxiliary and source domains during training. We use the meta-knowledge to analyze the shift between the target and source domains during testing. Specifically, we perform multiple transformations on source data to generate the auxiliary domain, perform counterfactual inference to learn to discover the causal factors of the shift between the auxiliary and source domains, and incorporate the inferred causality into factor-aware domain alignments. Extensive experiments on several benchmarks of image classification show the effectiveness of our method.

Self-supervised learning excels in learning representations from large amounts of unlabeled data, demonstrating success across multiple data modalities. Yet, extending self-supervised learning to new modalities is non-trivial because the specifics of existing methods are tailored to each domain, such as domain-specific augmentations which reflect the invariances in the target task. While masked modeling is promising as a domain-agnostic framework for self-supervised learning because it does not rely on input augmentations, its mask sampling procedure remains domain-specific. We present Self-guided Masked Autoencoders (SMA), a fully domain-agnostic masked modeling method. SMA trains an attention based model using a masked modeling objective, by learning masks to sample without any domain-specific assumptions. We evaluate SMA on three self-supervised learning benchmarks in protein biology, chemical property prediction, and particle physics. We find SMA is capable of learning representations without domain-specific knowledge and achieves state-of-the-art performance on these three benchmarks.

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X,Y) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X,Y). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

Human adaptability relies crucially on learning and merging knowledge from both supervised and unsupervised tasks: the parents point out few important concepts, but then the children fill in the gaps on their own. This is particularly effective, because supervised learning can never be exhaustive and thus learning autonomously allows to discover invariances and regularities that help to generalize. In this paper we propose to apply a similar approach to the problem of object recognition across domains: our model learns the semantic labels in a supervised fashion, and broadens its understanding of the data by learning from self-supervised signals on the same images. This secondary task helps the network to focus on object shapes, learning concepts like spatial orientation and part correlation, while acting as a regularizer for the classification task over multiple visual domains. Extensive experiments confirm our intuition and show that our multi-task method combining supervised and self-supervised knowledge shows competitive results with respect to more complex domain generalization and adaptation solutions. It also proves its potential in the novel and challenging predictive and partial domain adaptation scenarios.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Due to privacy, storage, and other constraints, there is a growing need for unsupervised domain adaptation techniques in machine learning that do not require access to the data used to train a collection of source models. Existing methods for multi-source-free domain adaptation (MSFDA) typically train a target model using pseudo-labeled data produced by the source models, which focus on improving the pseudo-labeling techniques or proposing new training objectives. Instead, we aim to analyze the fundamental limits of MSFDA. In particular, we develop an information-theoretic bound on the generalization error of the resulting target model, which illustrates an inherent bias-variance trade-off. We then provide insights on how to balance this trade-off from three perspectives, including domain aggregation, selective pseudo-labeling, and joint feature alignment, which leads to the design of novel algorithms. Experiments on multiple datasets validate our theoretical analysis and demonstrate the state-of-art performance of the proposed algorithm, especially on some of the most challenging datasets, including Office-Home and DomainNet.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

Domain Generation Algorithms (DGAs) are malicious techniques used by malware to dynamically generate seemingly random domain names for communication with Command & Control (C&C) servers. Due to the fast and simple generation of DGA domains, detection methods must be highly efficient and precise to be effective. Large Language Models (LLMs) have demonstrated their proficiency in real-time detection tasks, making them ideal candidates for detecting DGAs. Our work validates the effectiveness of fine-tuned LLMs for detecting DGAs and DNS exfiltration attacks. We developed LLM models and conducted comprehensive evaluation using a diverse dataset comprising 59 distinct real-world DGA malware families and normal domain data. Our LLM model significantly outperformed traditional natural language processing techniques, especially in detecting unknown DGAs. We also evaluated its performance on DNS exfiltration datasets, demonstrating its effectiveness in enhancing cybersecurity measures. To the best of our knowledge, this is the first work that empirically applies LLMs for DGA and DNS exfiltration detection.

Graph neural networks (GNNs) have achieved impressive performance in graph domain adaptation. However, extensive source graphs could be unavailable in real-world scenarios due to privacy and storage concerns. To this end, we investigate an underexplored yet practical problem of source-free graph domain adaptation, which transfers knowledge from source models instead of source graphs to a target domain. To solve this problem, we introduce a novel GNN-based approach called Rank and Align (RNA), which ranks graph similarities with spectral seriation for robust semantics learning, and aligns inharmonic graphs with harmonic graphs which close to the source domain for subgraph extraction. In particular, to overcome label scarcity, we employ the spectral seriation algorithm to infer the robust pairwise rankings, which can guide semantic learning using a similarity learning objective. To depict distribution shifts, we utilize spectral clustering and the silhouette coefficient to detect harmonic graphs, which the source model can easily classify. To reduce potential domain discrepancy, we extract domain-invariant subgraphs from inharmonic graphs by an adversarial edge sampling process, which guides the invariant learning of GNNs. Extensive experiments on several benchmark datasets demonstrate the effectiveness of our proposed RNA.

Convolutional neural networks (CNNs) have achieved great successes in many computer vision problems. Unlike existing works that designed CNN architectures to improve performance on a single task of a single domain and not generalizable, we present IBN-Net, a novel convolutional architecture, which remarkably enhances a CNN's modeling ability on one domain (e.g. Cityscapes) as well as its generalization capacity on another domain (e.g. GTA5) without finetuning. IBN-Net carefully integrates Instance Normalization (IN) and Batch Normalization (BN) as building blocks, and can be wrapped into many advanced deep networks to improve their performances. This work has three key contributions. (1) By delving into IN and BN, we disclose that IN learns features that are invariant to appearance changes, such as colors, styles, and virtuality/reality, while BN is essential for preserving content related information. (2) IBN-Net can be applied to many advanced deep architectures, such as DenseNet, ResNet, ResNeXt, and SENet, and consistently improve their performance without increasing computational cost. (3) When applying the trained networks to new domains, e.g. from GTA5 to Cityscapes, IBN-Net achieves comparable improvements as domain adaptation methods, even without using data from the target domain. With IBN-Net, we won the 1st place on the WAD 2018 Challenge Drivable Area track, with an mIoU of 86.18%.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.

Domain generalization is the task of learning models that generalize to unseen target domains. We propose a simple yet effective method for domain generalization, named cross-domain ensemble distillation (XDED), that learns domain-invariant features while encouraging the model to converge to flat minima, which recently turned out to be a sufficient condition for domain generalization. To this end, our method generates an ensemble of the output logits from training data with the same label but from different domains and then penalizes each output for the mismatch with the ensemble. Also, we present a de-stylization technique that standardizes features to encourage the model to produce style-consistent predictions even in an arbitrary target domain. Our method greatly improves generalization capability in public benchmarks for cross-domain image classification, cross-dataset person re-ID, and cross-dataset semantic segmentation. Moreover, we show that models learned by our method are robust against adversarial attacks and image corruptions.

Due to domain shift, machine learning systems typically fail to generalize well to domains different from those of training data, which is what domain generalization (DG) aims to address. Although various DG methods have been developed, most of them lack interpretability and require domain labels that are not available in many real-world scenarios. This paper presents a novel DG method, called HMOE: Hypernetwork-based Mixture of Experts (MoE), which does not rely on domain labels and is more interpretable. MoE proves effective in identifying heterogeneous patterns in data. For the DG problem, heterogeneity arises exactly from domain shift. HMOE uses hypernetworks taking vectors as input to generate experts' weights, which allows experts to share useful meta-knowledge and enables exploring experts' similarities in a low-dimensional vector space. We compare HMOE with other DG algorithms under a fair and unified benchmark-DomainBed. Our extensive experiments show that HMOE can divide mixed-domain data into distinct clusters that are surprisingly more consistent with human intuition than original domain labels. Compared to other DG methods, HMOE shows competitive performance and achieves SOTA results in some cases.

Adverse weather image translation belongs to the unsupervised image-to-image (I2I) translation task which aims to transfer adverse condition domain (eg, rainy night) to standard domain (eg, day). It is a challenging task because images from adverse domains have some artifacts and insufficient information. Recently, many studies employing Generative Adversarial Networks (GANs) have achieved notable success in I2I translation but there are still limitations in applying them to adverse weather enhancement. Symmetric architecture based on bidirectional cycle-consistency loss is adopted as a standard framework for unsupervised domain transfer methods. However, it can lead to inferior translation result if the two domains have imbalanced information. To address this issue, we propose a novel GAN model, i.e., AU-GAN, which has an asymmetric architecture for adverse domain translation. We insert a proposed feature transfer network ({T}-net) in only a normal domain generator (i.e., rainy night-> day) to enhance encoded features of the adverse domain image. In addition, we introduce asymmetric feature matching for disentanglement of encoded features. Finally, we propose uncertainty-aware cycle-consistency loss to address the regional uncertainty of a cyclic reconstructed image. We demonstrate the effectiveness of our method by qualitative and quantitative comparisons with state-of-the-art models. Codes are available at https://github.com/jgkwak95/AU-GAN.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Recent studies empirically demonstrate the positive relationship between the transferability of neural networks and the within-class variation of the last layer features. The recently discovered Neural Collapse (NC) phenomenon provides a new perspective of understanding such last layer geometry of neural networks. In this paper, we propose a novel metric, named Variability Collapse Index (VCI), to quantify the variability collapse phenomenon in the NC paradigm. The VCI metric is well-motivated and intrinsically related to the linear probing loss on the last layer features. Moreover, it enjoys desired theoretical and empirical properties, including invariance under invertible linear transformations and numerical stability, that distinguishes it from previous metrics. Our experiments verify that VCI is indicative of the variability collapse and the transferability of pretrained neural networks.

We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded F_{1}-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive a generalization bound that combines a covering number argument for compositionality, and the F_{1}-norm (or the related Barron norm) for large width adaptivity. We show that the global minimizer of the regularized loss of DNNs can fit for example the composition of two functions f^{*}=hcirc g from a small number of observations, assuming g is smooth/regular and reduces the dimensionality (e.g. g could be the modulo map of the symmetries of f^{*}), so that h can be learned in spite of its low regularity. The measures of regularity we consider is the Sobolev norm with different levels of differentiability, which is well adapted to the F_{1} norm. We compute scaling laws empirically and observe phase transitions depending on whether g or h is harder to learn, as predicted by our theory.

Domain generalization is critical for real-world applications of machine learning to microscopy images, including histopathology and fluorescence imaging. Artifacts in these modalities arise through a complex combination of factors relating to tissue collection and laboratory processing, as well as factors intrinsic to patient samples. In fluorescence imaging, these artifacts stem from variations across experimental batches. The complexity and subtlety of these artifacts make the enumeration of data domains intractable. Therefore, augmentation-based methods of domain generalization that require domain identifiers and manual fine-tuning are inadequate in this setting. To overcome this challenge, we introduce ContriMix, a domain generalization technique that learns to generate synthetic images by disentangling and permuting the biological content ("content") and technical variations ("attributes") in microscopy images. ContriMix does not rely on domain identifiers or handcrafted augmentations and makes no assumptions about the input characteristics of images. We assess the performance of ContriMix on two pathology datasets dealing with patch classification and Whole Slide Image label prediction tasks respectively (Camelyon17-WILDS and RCC subtyping), and one fluorescence microscopy dataset (RxRx1-WILDS). Without any access to domain identifiers at train or test time, ContriMix performs similar or better than current state-of-the-art methods in all these datasets, motivating its usage for microscopy image analysis in real-world settings where domain information is hard to come by. The code for ContriMix can be found at https://gitlab.com/huutan86/contrimix

Large-scale commercial platforms usually involve numerous business domains for diverse business strategies and expect their recommendation systems to provide click-through rate (CTR) predictions for multiple domains simultaneously. Existing promising and widely-used multi-domain models discover domain relationships by explicitly constructing domain-specific networks, but the computation and memory boost significantly with the increase of domains. To reduce computational complexity, manually grouping domains with particular business strategies is common in industrial applications. However, this pre-defined data partitioning way heavily relies on prior knowledge, and it may neglect the underlying data distribution of each domain, hence limiting the model's representation capability. Regarding the above issues, we propose an elegant and flexible multi-distribution modeling paradigm, named Adaptive Distribution Hierarchical Model (AdaptDHM), which is an end-to-end optimization hierarchical structure consisting of a clustering process and classification process. Specifically, we design a distribution adaptation module with a customized dynamic routing mechanism. Instead of introducing prior knowledge for pre-defined data allocation, this routing algorithm adaptively provides a distribution coefficient for each sample to determine which cluster it belongs to. Each cluster corresponds to a particular distribution so that the model can sufficiently capture the commonalities and distinctions between these distinct clusters. Extensive experiments on both public and large-scale Alibaba industrial datasets verify the effectiveness and efficiency of AdaptDHM: Our model achieves impressive prediction accuracy and its time cost during the training stage is more than 50% less than that of other models.

Out-of-distribution (OOD) generalization is critical for machine learning models deployed in the real world. However, achieving this can be fundamentally challenging, as it requires the ability to learn invariant features across different domains or environments. In this paper, we propose a novel framework HYPO (HYPerspherical OOD generalization) that provably learns domain-invariant representations in a hyperspherical space. In particular, our hyperspherical learning algorithm is guided by intra-class variation and inter-class separation principles -- ensuring that features from the same class (across different training domains) are closely aligned with their class prototypes, while different class prototypes are maximally separated. We further provide theoretical justifications on how our prototypical learning objective improves the OOD generalization bound. Through extensive experiments on challenging OOD benchmarks, we demonstrate that our approach outperforms competitive baselines and achieves superior performance. Code is available at https://github.com/deeplearning-wisc/hypo.

Top-performing deep architectures are trained on massive amounts of labeled data. In the absence of labeled data for a certain task, domain adaptation often provides an attractive option given that labeled data of similar nature but from a different domain (e.g. synthetic images) are available. Here, we propose a new approach to domain adaptation in deep architectures that can be trained on large amount of labeled data from the source domain and large amount of unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of "deep" features that are (i) discriminative for the main learning task on the source domain and (ii) invariant with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a simple new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation. Overall, the approach can be implemented with little effort using any of the deep-learning packages. The method performs very well in a series of image classification experiments, achieving adaptation effect in the presence of big domain shifts and outperforming previous state-of-the-art on Office datasets.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Domain generalization (DG) seeks to learn robust models that generalize well under unknown distribution shifts. As a critical aspect of DG, optimizer selection has not been explored in depth. Currently, most DG methods follow the widely used benchmark, DomainBed, and utilize Adam as the default optimizer for all datasets. However, we reveal that Adam is not necessarily the optimal choice for the majority of current DG methods and datasets. Based on the perspective of loss landscape flatness, we propose a novel approach, Flatness-Aware Minimization for Domain Generalization (FAD), which can efficiently optimize both zeroth-order and first-order flatness simultaneously for DG. We provide theoretical analyses of the FAD's out-of-distribution (OOD) generalization error and convergence. Our experimental results demonstrate the superiority of FAD on various DG datasets. Additionally, we confirm that FAD is capable of discovering flatter optima in comparison to other zeroth-order and first-order flatness-aware optimization methods.

Domain generalization (DG) aims to learn domain-generalizable models from one or multiple source domains that can perform well in unseen target domains. Despite its recent progress, most existing work suffers from the misalignment between the difficulty level of training samples and the capability of contemporarily trained models, leading to over-fitting or under-fitting in the trained generalization model. We design MoDify, a Momentum Difficulty framework that tackles the misalignment by balancing the seesaw between the model's capability and the samples' difficulties along the training process. MoDify consists of two novel designs that collaborate to fight against the misalignment while learning domain-generalizable models. The first is MoDify-based Data Augmentation which exploits an RGB Shuffle technique to generate difficulty-aware training samples on the fly. The second is MoDify-based Network Optimization which dynamically schedules the training samples for balanced and smooth learning with appropriate difficulty. Without bells and whistles, a simple implementation of MoDify achieves superior performance across multiple benchmarks. In addition, MoDify can complement existing methods as a plug-in, and it is generic and can work for different visual recognition tasks.

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

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Domain adaptation (DA) has drawn high interest for its capacity to adapt a model trained on labeled source data to perform well on unlabeled or weakly labeled target data from a different domain. Most common DA techniques require concurrent access to the input images of both the source and target domains. However, in practice, privacy concerns often impede the availability of source images in the adaptation phase. This is a very frequent DA scenario in medical imaging, where, for instance, the source and target images could come from different clinical sites. We introduce a source-free domain adaptation for image segmentation. Our formulation is based on minimizing a label-free entropy loss defined over target-domain data, which we further guide with a domain-invariant prior on the segmentation regions. Many priors can be derived from anatomical information. Here, a class ratio prior is estimated from anatomical knowledge and integrated in the form of a Kullback Leibler (KL) divergence in our overall loss function. Furthermore, we motivate our overall loss with an interesting link to maximizing the mutual information between the target images and their label predictions. We show the effectiveness of our prior aware entropy minimization in a variety of domain-adaptation scenarios, with different modalities and applications, including spine, prostate, and cardiac segmentation. Our method yields comparable results to several state of the art adaptation techniques, despite having access to much less information, as the source images are entirely absent in our adaptation phase. Our straightforward adaptation strategy uses only one network, contrary to popular adversarial techniques, which are not applicable to a source-free DA setting. Our framework can be readily used in a breadth of segmentation problems, and our code is publicly available: https://github.com/mathilde-b/SFDA

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {Haldane bundle dataset}, which consists of synthetically generated complex line bundles on the 2-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

Domain adversarial training has been ubiquitous for achieving invariant representations and is used widely for various domain adaptation tasks. In recent times, methods converging to smooth optima have shown improved generalization for supervised learning tasks like classification. In this work, we analyze the effect of smoothness enhancing formulations on domain adversarial training, the objective of which is a combination of task loss (eg. classification, regression, etc.) and adversarial terms. We find that converging to a smooth minima with respect to (w.r.t.) task loss stabilizes the adversarial training leading to better performance on target domain. In contrast to task loss, our analysis shows that converging to smooth minima w.r.t. adversarial loss leads to sub-optimal generalization on the target domain. Based on the analysis, we introduce the Smooth Domain Adversarial Training (SDAT) procedure, which effectively enhances the performance of existing domain adversarial methods for both classification and object detection tasks. Our analysis also provides insight into the extensive usage of SGD over Adam in the community for domain adversarial training.

The inability of deep learning models to handle data drawn from unseen distributions has sparked much interest in unsupervised out-of-distribution (U-OOD) detection, as it is crucial for reliable deep learning models. Despite considerable attention, theoretically-motivated approaches are few and far between, with most methods building on top of some form of heuristic. Recently, U-OOD was formalized in the context of data invariants, allowing a clearer understanding of how to characterize U-OOD, and methods leveraging affine invariants have attained state-of-the-art results on large-scale benchmarks. Nevertheless, the restriction to affine invariants hinders the expressiveness of the approach. In this work, we broaden the affine invariants formulation to a more general case and propose a framework consisting of a normalizing flow-like architecture capable of learning non-linear invariants. Our novel approach achieves state-of-the-art results on an extensive U-OOD benchmark, and we demonstrate its further applicability to tabular data. Finally, we show our method has the same desirable properties as those based on affine invariants.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and non-existence pieces of C.

Large-scale foundation models like CLIP have shown strong zero-shot generalization but struggle with domain shifts, limiting their adaptability. In our work, we introduce StyLIP, a novel domain-agnostic prompt learning strategy for Domain Generalization (DG). StyLIP disentangles visual style and content in CLIP`s vision encoder by using style projectors to learn domain-specific prompt tokens and combining them with content features. Trained contrastively, this approach enables seamless adaptation across domains, outperforming state-of-the-art methods on multiple DG benchmarks. Additionally, we propose AD-CLIP for unsupervised domain adaptation (DA), leveraging CLIP`s frozen vision backbone to learn domain-invariant prompts through image style and content features. By aligning domains in embedding space with entropy minimization, AD-CLIP effectively handles domain shifts, even when only target domain samples are available. Lastly, we outline future work on class discovery using prompt learning for semantic segmentation in remote sensing, focusing on identifying novel or rare classes in unstructured environments. This paves the way for more adaptive and generalizable models in complex, real-world scenarios.

Multi-source domain adaptation has been intensively studied. The distribution shift in features inherent to specific domains causes the negative transfer problem, degrading a model's generality to unseen tasks. In Federated Learning (FL), learned model parameters are shared to train a global model that leverages the underlying knowledge across client models trained on separate data domains. Nonetheless, the data confidentiality of FL hinders the effectiveness of traditional domain adaptation methods that require prior knowledge of different domain data. We propose a new federated domain generalization method called Federated Knowledge Alignment (FedKA). FedKA leverages feature distribution matching in a global workspace such that the global model can learn domain-invariant client features under the constraint of unknown client data. FedKA employs a federated voting mechanism that generates target domain pseudo-labels based on the consensus from clients to facilitate global model fine-tuning. We performed extensive experiments, including an ablation study, to evaluate the effectiveness of the proposed method in both image and text classification tasks using different model architectures. The empirical results show that FedKA achieves performance gains of 8.8% and 3.5% in Digit-Five and Office-Caltech10, respectively, and a gain of 0.7% in Amazon Review with extremely limited training data. Moreover, we studied the effectiveness of FedKA in alleviating the negative transfer of FL based on a new criterion called Group Effect. The results show that FedKA can reduce negative transfer, improving the performance gain via model aggregation by 4 times.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of target data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at https://github.com/BIT-DA/EADA.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data, planar rotations of the input will result in correspondingly rotated outputs. It is therefore desirable that deep learning models be rotationally equivariant. In addition, contours are typically represented as an ordered sequence of edge points, where the choice of starting point is arbitrary. It is therefore also desirable for deep learning methods to be equivariant under cyclic shifts. We present RotaTouille, a deep learning framework for learning from contour data that achieves both rotation and cyclic shift equivariance through complex-valued circular convolution. We further introduce and characterize equivariant non-linearities, coarsening layers, and global pooling layers to obtain invariant representations for downstream tasks. Finally, we demonstrate the effectiveness of RotaTouille through experiments in shape classification, reconstruction, and contour regression.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

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

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Automated polyp segmentation is essential for early diagnosis of colorectal cancer, yet developing robust models remains challenging due to limited annotated data and significant performance degradation under domain shift. Although semi-supervised learning (SSL) reduces annotation requirements, existing methods rely on generic augmentations that ignore polyp-specific structural properties, resulting in poor generalization to new imaging centers and devices. To address this, we introduce Frequency Prior Guided Matching (FPGM), a novel augmentation framework built on a key discovery: polyp edges exhibit a remarkably consistent frequency signature across diverse datasets. FPGM leverages this intrinsic regularity in a two-stage process. It first learns a domain-invariant frequency prior from the edge regions of labeled polyps. Then, it performs principled spectral perturbations on unlabeled images, aligning their amplitude spectra with this learned prior while preserving phase information to maintain structural integrity. This targeted alignment normalizes domain-specific textural variations, thereby compelling the model to learn the underlying, generalizable anatomical structure. Validated on six public datasets, FPGM establishes a new state-of-the-art against ten competing methods. It demonstrates exceptional zero-shot generalization capabilities, achieving over 10% absolute gain in Dice score in data-scarce scenarios. By significantly enhancing cross-domain robustness, FPGM presents a powerful solution for clinically deployable polyp segmentation under limited supervision.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of K-sparse degree-d PTFs on R^n, where any such concept depends only on K out of n attributes of the input. Our main contribution is a new algorithm that runs in time ({nd}/{epsilon})^{O(d)} and under the Gaussian marginal distribution, PAC learns the class up to error rate epsilon with O(K^{4d}{epsilon^{2d}} cdot log^{5d} n) samples even when an eta leq O(epsilon^d) fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-2d polynomial as a filter to detect corrupted samples.

Linear Mode Connectivity (LMC) refers to the phenomenon that performance remains consistent for linearly interpolated models in the parameter space. For independently optimized model pairs from different random initializations, achieving LMC is considered crucial for validating the stable success of the non-convex optimization in modern machine learning models and for facilitating practical parameter-based operations such as model merging. While LMC has been achieved for neural networks by considering the permutation invariance of neurons in each hidden layer, its attainment for other models remains an open question. In this paper, we first achieve LMC for soft tree ensembles, which are tree-based differentiable models extensively used in practice. We show the necessity of incorporating two invariances: subtree flip invariance and splitting order invariance, which do not exist in neural networks but are inherent to tree architectures, in addition to permutation invariance of trees. Moreover, we demonstrate that it is even possible to exclude such additional invariances while keeping LMC by designing decision list-based tree architectures, where such invariances do not exist by definition. Our findings indicate the significance of accounting for architecture-specific invariances in achieving LMC.

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes' theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA

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

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of dimensionality. However, most prior theoretical analyses have been limited to linear PDEs. In this work, we take a step towards studying the representational power of neural networks for approximating solutions to nonlinear PDEs. We focus on a class of PDEs known as nonlinear elliptic variational PDEs, whose solutions minimize an Euler-Lagrange energy functional E(u) = int_Omega L(x, u(x), nabla u(x)) - f(x) u(x)dx. We show that if composing a function with Barron norm b with partial derivatives of L produces a function of Barron norm at most B_L b^p, the solution to the PDE can be epsilon-approximated in the L^2 sense by a function with Barron norm Oleft(left(dB_Lright)^{max{p log(1/ epsilon), p^{log(1/epsilon)}}}right). By a classical result due to Barron [1993], this correspondingly bounds the size of a 2-layer neural network needed to approximate the solution. Treating p, epsilon, B_L as constants, this quantity is polynomial in dimension, thus showing neural networks can evade the curse of dimensionality. Our proof technique involves neurally simulating (preconditioned) gradient in an appropriate Hilbert space, which converges exponentially fast to the solution of the PDE, and such that we can bound the increase of the Barron norm at each iterate. Our results subsume and substantially generalize analogous prior results for linear elliptic PDEs over a unit hypercube.

Single-source domain generalization attempts to learn a model on a source domain and deploy it to unseen target domains. Limiting access only to source domain data imposes two key challenges - how to train a model that can generalize and how to verify that it does. The standard practice of validation on the training distribution does not accurately reflect the model's generalization ability, while validation on the test distribution is a malpractice to avoid. In this work, we construct an independent validation set by transforming source domain images with a comprehensive list of augmentations, covering a broad spectrum of potential distribution shifts in target domains. We demonstrate a high correlation between validation and test performance for multiple methods and across various datasets. The proposed validation achieves a relative accuracy improvement over the standard validation equal to 15.4% or 1.6% when used for method selection or learning rate tuning, respectively. Furthermore, we introduce a novel family of methods that increase the shape bias through enhanced edge maps. To benefit from the augmentations during training and preserve the independence of the validation set, a k-fold validation process is designed to separate the augmentation types used in training and validation. The method that achieves the best performance on the augmented validation is selected from the proposed family. It achieves state-of-the-art performance on various standard benchmarks. Code at: https://github.com/NikosEfth/crafting-shifts

The Shadowing Principle of Manin has proved a valuable tool for addressing questions of quantitative topology raised by Gromov in the late 1900s. The principle informally provides a way for bounded algebraic maps between differential graded algebras to be translated into nearby genuine maps between their geometric realizations. We extend this principle to finite towers of principal K(G,n) fibrations, and in particular apply this construction to nilpotent spaces. As a specific application of the extended principle, we provide upper bounds on the asymptotic behavior of volumes of nullhomotopies of Lipschitz maps into nilpotent spaces. We further refine these bounds in the case when c = 1 to nearly meet those of the simply connected setting. We similarly refine these bounds in the event the target space is coformal, and demonstrate that the bounds in this setting are nearly sharp.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

One persistent obstacle in industrial quality inspection is the detection of anomalies. In real-world use cases, two problems must be addressed: anomalous data is sparse and the same types of anomalies need to be detected on previously unseen objects. Current anomaly detection approaches can be trained with sparse nominal data, whereas domain generalization approaches enable detecting objects in previously unseen domains. Utilizing those two observations, we introduce the hybrid task of domain generalization on sparse classes. To introduce an accompanying dataset for this task, we present a modification of the well-established MVTec AD dataset by generating three new datasets. In addition to applying existing methods for benchmark, we design two embedding-based approaches, Spatial Embedding MLP (SEMLP) and Labeled PatchCore. Overall, SEMLP achieves the best performance with an average image-level AUROC of 87.2 % vs. 80.4 % by MIRO. The new and openly available datasets allow for further research to improve industrial anomaly detection.

Conventional supervised learning typically assumes that the learning task can be solved by learning a single function since the data is sampled from a fixed distribution. However, this assumption is invalid in open-ended environments where no task-level data partitioning is available. In this paper, we present a novel supervised learning framework of learning from open-ended data, which is modeled as data implicitly sampled from multiple domains with the data in each domain obeying a domain-specific target function. Since different domains may possess distinct target functions, open-ended data inherently requires multiple functions to capture all its input-output relations, rendering training a single global model problematic. To address this issue, we devise an Open-ended Supervised Learning (OSL) framework, of which the key component is a subjective function that allocates the data among multiple candidate models to resolve the "conflict" between the data from different domains, exhibiting a natural hierarchy. We theoretically analyze the learnability and the generalization error of OSL, and empirically validate its efficacy in both open-ended regression and classification tasks.

Deep neural networks are known to be vulnerable to security risks due to the inherent transferable nature of adversarial examples. Despite the success of recent generative model-based attacks demonstrating strong transferability, it still remains a challenge to design an efficient attack strategy in a real-world strict black-box setting, where both the target domain and model architectures are unknown. In this paper, we seek to explore a feature contrastive approach in the frequency domain to generate adversarial examples that are robust in both cross-domain and cross-model settings. With that goal in mind, we propose two modules that are only employed during the training phase: a Frequency-Aware Domain Randomization (FADR) module to randomize domain-variant low- and high-range frequency components and a Frequency-Augmented Contrastive Learning (FACL) module to effectively separate domain-invariant mid-frequency features of clean and perturbed image. We demonstrate strong transferability of our generated adversarial perturbations through extensive cross-domain and cross-model experiments, while keeping the inference time complexity.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) Non-uniqueness: there are many different eigendecompositions of the same Laplacian, and (2) Instability: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability and continuity to higher-order functions, so that we can formulate novel convergence criteria for regression, derived from the convergence of global optimisation. All the theory and the motivating examples are fully formalised in the proof assistant Agda.

Gross, Mansour, and Tucker introduced the partial-duality polynomial of a ribbon graph [Distributions, European J. Combin. 86, 1--20, 2020], the generating function enumerating partial duals by the Euler genus. Chmutov and Vignes-Tourneret wondered if this polynomial and its conjectured properties would hold for general delta-matroids, which are combinatorial abstractions of ribbon graphs. Yan and Jin contributed to this inquiry by identifying a subset of delta-matroids-specifically, even normal binary ones-whose twist polynomials are characterized by a singular term. Building upon this foundation, the current paper expands the scope of the investigation to encompass even non-binary delta-matroids, revealing that none of them have width-changing twists.

Generalisation of deep neural networks becomes vulnerable when distribution shifts are encountered between train (source) and test (target) domain data. Few-shot domain adaptation mitigates this issue by adapting deep neural networks pre-trained on the source domain to the target domain using a randomly selected and annotated support set from the target domain. This paper argues that randomly selecting the support set can be further improved for effectively adapting the pre-trained source models to the target domain. Alternatively, we propose SelectNAdapt, an algorithm to curate the selection of the target domain samples, which are then annotated and included in the support set. In particular, for the K-shot adaptation problem, we first leverage self-supervision to learn features of the target domain data. Then, we propose a per-class clustering scheme of the learned target domain features and select K representative target samples using a distance-based scoring function. Finally, we bring our selection setup towards a practical ground by relying on pseudo-labels for clustering semantically similar target domain samples. Our experiments show promising results on three few-shot domain adaptation benchmarks for image recognition compared to related approaches and the standard random selection.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

In recent years, there has been a development in approaching rationality problems through the motivic methods (cf. [Kontsevich--Tschinkel'19], [Nicaise--Shinder'19], [Nicaise--Ottem'21]). This method requires the explicit construction of degeneration families of curves with favorable properties. While the specific construction is generally difficult, [Nicaise--Ottem'22] combines combinatorial methods to construct degeneration families of hypersurfaces in toric varieties and shows the non-stable rationality of a very general hypersurface in projective spaces. In this paper, we extend the result of [Nicaise--Ottem'22] not only for hypersurfaces in algebraic tori but also to those in sch\"{o}n affine varieties. In application, we show the irrationality of certain hypersurfaces in the complex Grassmannian variety Gr(2, n) using the motivic method, which coincides with the result obtained by the same author in the previous research.

Deep neural networks (DNNs) often perform poorly in the presence of domain shift and category shift. How to upcycle DNNs and adapt them to the target task remains an important open problem. Unsupervised Domain Adaptation (UDA), especially recently proposed Source-free Domain Adaptation (SFDA), has become a promising technology to address this issue. Nevertheless, existing SFDA methods require that the source domain and target domain share the same label space, consequently being only applicable to the vanilla closed-set setting. In this paper, we take one step further and explore the Source-free Universal Domain Adaptation (SF-UniDA). The goal is to identify "known" data samples under both domain and category shift, and reject those "unknown" data samples (not present in source classes), with only the knowledge from standard pre-trained source model. To this end, we introduce an innovative global and local clustering learning technique (GLC). Specifically, we design a novel, adaptive one-vs-all global clustering algorithm to achieve the distinction across different target classes and introduce a local k-NN clustering strategy to alleviate negative transfer. We examine the superiority of our GLC on multiple benchmarks with different category shift scenarios, including partial-set, open-set, and open-partial-set DA. Remarkably, in the most challenging open-partial-set DA scenario, GLC outperforms UMAD by 14.8\% on the VisDA benchmark. The code is available at https://github.com/ispc-lab/GLC.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

This article establishes a complete approximate axiomatization for the real-closed field R expanded with all differentially-defined functions, including special functions such as sin(x), cos(x), e^x, dots. Every true sentence is provable up to some numerical approximation, and the truth of such approximations converge under mild conditions. Such an axiomatization is a fragment of the axiomatization for differential dynamic logic, and is therefore a finite extension of the axiomatization of real-closed fields. Furthermore, the numerical approximations approximate formulas containing special function symbols by FOL_{R} formulas, improving upon earlier decidability results only concerning closed sentences.

Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.

Iris-based biometric systems are vulnerable to presentation attacks (PAs), where adversaries present physical artifacts (e.g., printed iris images, textured contact lenses) to defeat the system. This has led to the development of various presentation attack detection (PAD) algorithms, which typically perform well in intra-domain settings. However, they often struggle to generalize effectively in cross-domain scenarios, where training and testing employ different sensors, PA instruments, and datasets. In this work, we use adversarial training samples of both bonafide irides and PAs to improve the cross-domain performance of a PAD classifier. The novelty of our approach lies in leveraging transformation parameters from classical data augmentation schemes (e.g., translation, rotation) to generate adversarial samples. We achieve this through a convolutional autoencoder, ADV-GEN, that inputs original training samples along with a set of geometric and photometric transformations. The transformation parameters act as regularization variables, guiding ADV-GEN to generate adversarial samples in a constrained search space. Experiments conducted on the LivDet-Iris 2017 database, comprising four datasets, and the LivDet-Iris 2020 dataset, demonstrate the efficacy of our proposed method. The code is available at https://github.com/iPRoBe-lab/ADV-GEN-IrisPAD.

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

To represent the biological variability of clinical neuroimaging populations, it is vital to be able to combine data across scanners and studies. However, different MRI scanners produce images with different characteristics, resulting in a domain shift known as the `harmonisation problem'. Additionally, neuroimaging data is inherently personal in nature, leading to data privacy concerns when sharing the data. To overcome these barriers, we propose an Unsupervised Source-Free Domain Adaptation (SFDA) method, SFHarmony. Through modelling the imaging features as a Gaussian Mixture Model and minimising an adapted Bhattacharyya distance between the source and target features, we can create a model that performs well for the target data whilst having a shared feature representation across the data domains, without needing access to the source data for adaptation or target labels. We demonstrate the performance of our method on simulated and real domain shifts, showing that the approach is applicable to classification, segmentation and regression tasks, requiring no changes to the algorithm. Our method outperforms existing SFDA approaches across a range of realistic data scenarios, demonstrating the potential utility of our approach for MRI harmonisation and general SFDA problems. Our code is available at https://github.com/nkdinsdale/SFHarmony.

Addressing fairness in artificial intelligence (AI), particularly in medical AI, is crucial for ensuring equitable healthcare outcomes. Recent efforts to enhance fairness have introduced new methodologies and datasets in medical AI. However, the fairness issue under the setting of domain transfer is almost unexplored, while it is common that clinics rely on different imaging technologies (e.g., different retinal imaging modalities) for patient diagnosis. This paper presents FairDomain, a pioneering systemic study into algorithmic fairness under domain shifts, employing state-of-the-art domain adaptation (DA) and generalization (DG) algorithms for both medical segmentation and classification tasks to understand how biases are transferred between different domains. We also introduce a novel plug-and-play fair identity attention (FIA) module that adapts to various DA and DG algorithms to improve fairness by using self-attention to adjust feature importance based on demographic attributes. Additionally, we curate the first fairness-focused dataset with two paired imaging modalities for the same patient cohort on medical segmentation and classification tasks, to rigorously assess fairness in domain-shift scenarios. Excluding the confounding impact of demographic distribution variation between source and target domains will allow clearer quantification of the performance of domain transfer models. Our extensive evaluations reveal that the proposed FIA significantly enhances both model performance accounted for fairness across all domain shift settings (i.e., DA and DG) with respect to different demographics, which outperforms existing methods on both segmentation and classification. The code and data can be accessed at https://ophai.hms.harvard.edu/datasets/harvard-fairdomain20k.

We present an elementary, self-contained proof of Grothendieck's inequality that unifies the real and complex cases and yields both the Krivine and Haagerup bounds, the current best-known explicit bounds for the real and complex Grothendieck constants respectively. This article is intended to be pedagogical, combining and streamlining known ideas of Lindenstrauss--Pe{\l}czy\'nski, Krivine, and Haagerup into a proof that need only univariate calculus, basic complex variables, and a modicum of linear algebra as prerequisites.

Object detectors have achieved remarkable performance in many applications; however, these deep learning models are typically designed under the i.i.d. assumption, meaning they are trained and evaluated on data sampled from the same (source) distribution. In real-world deployment, however, target distributions often differ from source data, leading to substantial performance degradation. Domain Generalisation (DG) seeks to bridge this gap by enabling models to generalise to Out-Of-Distribution (OOD) data without access to target distributions during training, enhancing robustness to unseen conditions. In this work, we examine the generalisability and robustness of state-of-the-art object detectors under real-world distribution shifts, focusing particularly on spatial domain shifts. Despite the need, a standardised benchmark dataset specifically designed for assessing object detection under realistic DG scenarios is currently lacking. To address this, we introduce Real-World Distribution Shifts (RWDS), a suite of three novel DG benchmarking datasets that focus on humanitarian and climate change applications. These datasets enable the investigation of domain shifts across (i) climate zones and (ii) various disasters and geographic regions. To our knowledge, these are the first DG benchmarking datasets tailored for object detection in real-world, high-impact contexts. We aim for these datasets to serve as valuable resources for evaluating the robustness and generalisation of future object detection models. Our datasets and code are available at https://github.com/RWGAI/RWDS.

Accelerating material discovery holds the potential to greatly help mitigate the climate crisis. Discovering new solid-state materials such as electrocatalysts, super-ionic conductors or photovoltaic materials can have a crucial impact, for instance, in improving the efficiency of renewable energy production and storage. In this paper, we introduce Crystal-GFN, a generative model of crystal structures that sequentially samples structural properties of crystalline materials, namely the space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physical and structural hard constraints, as well as the use of any available predictive model of a desired physicochemical property as an objective function. To design stable materials, one must target the candidates with the lowest formation energy. Here, we use as objective the formation energy per atom of a crystal structure predicted by a new proxy machine learning model trained on MatBench. The results demonstrate that Crystal-GFN is able to sample highly diverse crystals with low (median -3.1 eV/atom) predicted formation energy.