Invariant Representation Learning

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Invariant representation learning studies how to encode data so that changes such as viewpoint, sensor, speaker, environment, or input format do not obscure task-relevant information. Approaches include symmetry-aware architectures, contrastive and predictive self-supervision, and methods that disentangle stable features from domain-specific variation or align representations across environments. These ideas are used in vision, graphs, speech, biomedical signals, robotics, and scientific data, often evaluated on shifted domains, unseen transformations, or cross-subject and cross-device benchmarks. A central tension is that removing variation can improve robustness but also discard useful signal; invariance alone does not guarantee reliable transfer, fairness, or generalization when the target itself changes across environments.

Latest papers

229 papers33 papers in the last four weeks, up 50% on the four weeks before. 0.2% of all new papers.

Mar 31, 2026

Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels

Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic (Power et al., 2022). We study grokking on algebraic tasks in a class of feature learning kernels via the Recursive Feature Machine (RFM) algorithm (Radhakrishnan et al., 2024), which iteratively updates feature matrices through the Average Gradient Outer Product (AGOP) of an estimator in order to learn task-relevant features. Our main experimental finding is that generalization occurs only when a certain symmetry in the training set is broken. Furthermore, we empirically show that RFM generalizes by recovering the underlying invariance group action inherent in the data. We find that the learned feature matrices encode specific elements of the invariance group, explaining the dependence of generalization on symmetry.

Marcel Tomàs Bernal, Neil Rohit Mallinar, Mikhail Belkin

CFIS UPC · UC San Diego

Symmetry Breaking Kernel Methods Invariant Representation Learning Grokking

Mar 31, 2026

Suppressing Non-Semantic Noise in Masked Image Modeling Representations

Masked Image Modeling (MIM) has become a ubiquitous self-supervised vision paradigm. In this work, we show that MIM objectives cause the learned representations to retain non-semantic information, which ultimately hurts performance during inference. We introduce a model-agnostic score for semantic invariance using Principal Component Analysis (PCA) on real and synthetic non-semantic images. Based on this score, we propose a simple method, Semantically Orthogonal Artifact Projection (SOAP), to directly suppress non-semantic information in patch representations, leading to consistent improvements in zero-shot performance across various MIM-based models. SOAP is a post-hoc suppression method, requires zero training, and can be attached to any model as a single linear head.

Martine Hjelkrem-Tan, Marius Aasan, Rwiddhi Chakraborty +3

University of Oslo · UiT The Arctic University of Norway

Self-Supervised Visual Representation Learning Masked Image Modeling Invariant Representation Learning

Mar 29, 2026

RINO: Rotation-Invariant Non-Rigid Correspondences

Dense 3D shape correspondence remains a central challenge in computer vision and graphics as many deep learning approaches still rely on intermediate geometric features or handcrafted descriptors, limiting their effectiveness under non-isometric deformations, partial data, and non-manifold inputs. To overcome these issues, we introduce RINO, an unsupervised, rotation-invariant dense correspondence framework that effectively unifies rigid and non-rigid shape matching. The core of our method is the novel RINONet, a feature extractor that integrates vector-based SO(3)-invariant learning with orientation-aware complex functional maps to extract robust features directly from raw geometry. This allows for a fully end-to-end, data-driven approach that bypasses the need for shape pre-alignment or handcrafted features. Extensive experiments show unprecedented performance of RINO across challenging non-rigid matching tasks, including arbitrary poses, non-isometry, partiality, non-manifoldness, and noise.

Maolin Gao, Shao Jie Hu-Chen, Congyue Deng +3

TUM · MCML · Stanford University +1

Functional Maps Non-Rigid Shape Correspondence 3D Shape Matching Invariant Representation Learning

Mar 29, 2026

On the Asymptotics of Self-Supervised Pre-training: Two-Stage M-Estimation and Representation Symmetry

Self-supervised pre-training, where large corpora of unlabeled data are used to learn representations for downstream fine-tuning, has become a cornerstone of modern machine learning. While a growing body of theoretical work has begun to analyze this paradigm, existing bounds leave open the question of how sharp the current rates are, and whether they accurately capture the complex interaction between pre-training and fine-tuning. In this paper, we address this gap by developing an asymptotic theory of pre-training via two-stage M-estimation. A key challenge is that the pre-training estimator is often identifiable only up to a group symmetry, a feature common in representation learning that requires careful treatment. We address this issue using tools from Riemannian geometry to study the intrinsic parameters of the pre-training representation, which we link with the downstream predictor through a notion of orbit-invariance, precisely characterizing the limiting distribution of the downstream test risk. We apply our main result to several case studies, including spectral pre-training, factor models, and Gaussian mixture models, and obtain substantial improvements in problem-specific factors over prior art when applicable.

Mohammad Tinati, Stephen Tu

Department of Electrical and Computer Engineering, University of Southern California

Self-Supervised Pre-Training Invariant Representation Learning Statistical Learning Theory

Mar 26, 2026

When Sensing Varies with Contexts: Context Probing for Tactile Few-Shot Class-Incremental Learning

Few-shot class-incremental learning (FSCIL) aims to recognize novel classes from only a few labeled samples while retaining previously learned knowledge. Although recent FSCIL methods have achieved substantial progress on visual benchmarks, they remain limited in tactile sensing, where the same material may produce markedly different observations under different acquisition contexts, such as sensing devices, contact states, scanning trajectories, and interaction conditions. In tactile FSCIL, the challenges of few-shot learning and class-incremental learning are further amplified by acquisition context: the limited support samples may not only be scarce, but also carry context-induced biases. Once the resulting biased prototypes are inserted into the classifier, they may affect the decision boundaries in subsequent sessions. To address this problem, we propose Context-Probing Few-Shot Class-Incremental Learning (CoP-FSCIL), a context-aware framework for tactile FSCIL. CoP-FSCIL first employs Context-Probing Intervention (CPI) to diagnose local context-sensitive variations in tactile representations. It then introduces a Probe-Conditioned Quotient Adapter (PCQA) to suppress context-sensitive components identified by the probes. Finally, Probe-Stability Prototype Calibration (PSPC) estimates support sample reliability from probe-induced embedding fluctuations and calibrates stochastic prototypes accordingly. Experiments on HapTex and LMT108 show that CoP-FSCIL consistently outperforms representative FSCIL baselines, and extended experiments on audio FSCIL further demonstrate the generality of the proposed context probing mechanism. The source code is currently being prepared and will be released soon.

Yifeng Lin, Aiping Huang, Wenxi Liu +4

Fujian Key Laboratory for Intelligent Processing and Wireless Transmission of Media Information, College of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, China

Class-Incremental Learning Prototype-Based Classification Tactile Sensing Few-Shot Learning Invariant Representation Learning

Mar 26, 2026

Learning domain-invariant features through channel-level sparsification for Out-Of Distribution Generalization

Out-of-Distribution (OOD) generalization has become a primary metric for evaluating image analysis systems. Since deep learning models tend to capture domain-specific context, they often develop shortcut dependencies on these non-causal features, leading to inconsistent performance across different data sources. Current techniques, such as invariance learning, attempt to mitigate this. However, they struggle to isolate highly mixed features within deep latent spaces. This limitation prevents them from fully resolving the shortcut learning problem.In this paper, we propose Hierarchical Causal Dropout (HCD), a method that uses channel-level causal masks to enforce feature sparsity. This approach allows the model to separate causal features from spurious ones, effectively performing a causal intervention at the representation level. The training is guided by a Matrix-based Mutual Information (MMI) objective to minimize the mutual information between latent features and domain labels, while simultaneously maximizing the information shared with class labels.To ensure stability, we incorporate a StyleMix-driven VICReg module, which prevents the masks from accidentally filtering out essential causal data. Experimental results on OOD benchmarks show that HCD performs better than existing top-tier methods.

Haoran Pei, Yuguang Yang, Kexin Liu +2

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, P. R. China · School of Electronic Information Engineering, Beihang University, Beijing 100191, P. R. China · School of Artificial Intelligence, Beihang University, Beijing 100191, P. R. China

OOD Generalization Invariant Representation Learning Shortcut Learning Causal Representation Learning

Mar 24, 2026

Multi-Modal Image Fusion via Intervention-Stable Feature Learning

Multi-modal image fusion integrates complementary information from different modalities into a unified representation. Current methods predominantly optimize statistical correlations between modalities, often capturing dataset-induced spurious associations that degrade under distribution shifts. In this paper, we propose an intervention-based framework inspired by causal principles to identify robust cross-modal dependencies. Drawing insights from Pearl's causal hierarchy, we design three principled intervention strategies to probe different aspects of modal relationships: i) complementary masking with spatially disjoint perturbations tests whether modalities can genuinely compensate for each other's missing information, ii) random masking of identical regions identifies feature subsets that remain informative under partial observability, and iii) modality dropout evaluates the irreplaceable contribution of each modality. Based on these interventions, we introduce a Causal Feature Integrator (CFI) that learns to identify and prioritize intervention-stable features maintaining importance across different perturbation patterns through adaptive invariance gating, thereby capturing robust modal dependencies rather than spurious correlations. Extensive experiments demonstrate that our method achieves SOTA performance on both public benchmarks and downstream high-level vision tasks.

Xue Wang, Zheng Guan, Wenhua Qian +2

School of Information Science and Engineering, Yunnan University · School of Artificial Intelligence, Nanyang Normal University · Department of Electrical and Electronic Engineering, Hong Kong Polytechnic University

Multi-Source Image Fusion Multimodal Robustness Invariant Representation Learning Causal Representation Learning

Mar 23, 2026

Generalized multi-object classification and tracking with sparse feature resonator networks

In visual scene understanding tasks, it is essential to capture both invariant and equivariant structure. While neural networks are frequently trained to achieve invariance to transformations such as translation, this often comes at the cost of losing access to equivariant information - e.g., the precise location of an object. Moreover, invariance is not naturally guaranteed through supervised learning alone, and many architectures generalize poorly to input transformations not encountered during training. Here, we take an approach based on analysis-by-synthesis and factoring using resonator networks. A generative model describes the construction of simple scenes containing MNIST digits and their transformations, like color and position. The resonator network inverts the generative model, and provides both invariant and equivariant information about particular objects. Sparse features learned from training data act as a basis set to provide flexibility in representing variable shapes of objects, allowing the resonator network to handle previously unseen digit shapes from the test set. The modular structure provides a shape module which contains information about the object shape with translation factored out, allowing a simple classifier to operate on centered digits. The classification layer is trained solely on centered data, requiring much less training data, and the network as a whole can identify objects with arbitrary translations without data augmentation. The natural attention-like mechanism of the resonator network also allows for analysis of scenes with multiple objects, where the network dynamics selects and centers only one object at a time. Further, the specific position information of a particular object can be extracted from the translation module, and we show that the resonator can be designed to track multiple moving objects with precision of a few pixels.

Lazar Supic, Alec Mullen, E. Paxon Frady

Redwood Center for Theoretical Neuroscience, UC Berkeley · Neuromorphic Computing Lab, Intel

Object-Centric Representation Learning Multi-Object Tracking Invariant Representation Learning Equivariant Representation Learning

Mar 23, 2026

Show Me What You Don't Know: Efficient Sampling from Invariant Sets for Model Validation

The performance of machine learning models depends on discovering features in the data that are relevant to solving the given task while ignoring irrelevant variation. To check and visualize whether this is the case, we propose 'invariance auditing', a diagnostic tool to analyze feature extractors. Invariance auditing generates diverse inputs which all yield the same features as a given query input, and are therefore treated as identical by the model. Using external knowledge about the task at hand, this enables assessing if the learned invariances do or do not conform to the task's required semantics. Unlike existing work where a dedicated generative model is trained for each feature extractor, our algorithm is training-free and exploits a pretrained diffusion or flow-matching model to sample invariant inputs. Our fiber loss -- which penalizes feature mismatch -- guides the denoising process so the output shares the same representation as the query input. This replaces days of training with a single guided generation procedure at comparable quality. Experiments on popular datasets and model types demonstrate that our auditing method reveals invariances spanning very desirable and concerning behavior. For instance, it detects cases where Qwen-2B places patients with situs inversus (heart on the right side) in the same fiber as typical anatomy. Our code is available at https://github.com/vislearn/InvarianceAuditing.

Armand Rousselot, Joran Wendebourg, Ullrich Köthe

Computer Vision and Learning Lab, Heidelberg University.

Feature Visualization Invariant Representation Learning Diffusion Sampling

Mar 17, 2026

GIST: Gauge-Invariant Spectral Transformers for Scalable Graph Neural Operators

Neural operators on irregular meshes face a fundamental tension. Spectral positional encodings, the natural choice for capturing geometry, require cubic-complexity eigendecomposition and inadvertently break gauge invariance through numerical solver artifacts; existing efficient approximations sacrifice gauge symmetry by design. Both failure modes break discretization invariance: models fail to transfer across mesh resolutions of the same domain, and similarly across different graphs of related structure in inductive settings. We propose GIST (Gauge-Invariant Spectral Transformer), a scalable neural operator that resolves this tension by restricting attention to pairwise inner products of efficient approximate spectral embeddings. We prove these inner products estimate an exactly gauge-invariant graph kernel at end-to-end

\mathcal{O}(N)

complexity, and establish a formal connection between gauge invariance and discretization-invariant learning with bounded mismatch error. To our knowledge, GIST is the first scalable graph neural operator with a provable discretization-mismatch bound. Empirically, GIST sets state-of-the-art on the AirfRANS, ShapeNet-Car, DrivAerNet, and DrivAerNet++ mesh benchmarks (up to 750K nodes), and additionally matches strong baselines on standard graph benchmarks (e.g., 99.50% micro-F1 on PPI).

Mattia Rigotti, Nicholas Thumiger, Thomas Frick

IBM Research

Graph Neural Operators Neural Operators Spectral Methods Invariant Representation Learning

Mar 17, 2026

GATS: Gaussian Aware Temporal Scaling Transformer for Invariant 4D Spatio-Temporal Point Cloud Representation

Understanding 4D point cloud videos is essential for enabling intelligent agents to perceive dynamic environments. However, temporal scale bias across varying frame rates and distributional uncertainty in irregular point clouds make it highly challenging to design a unified and robust 4D backbone. Existing CNN or Transformer based methods are constrained either by limited receptive fields or by quadratic computational complexity, while neglecting these implicit distortions. To address this problem, we propose a novel dual invariant framework, termed Gaussian Aware Temporal Scaling (GATS), which explicitly resolves both distributional inconsistencies and temporal. The proposed Uncertainty Guided Gaussian Convolution (UGGC) incorporates local Gaussian statistics and uncertainty aware gating into point convolution, thereby achieving robust neighborhood aggregation under density variation, noise, and occlusion. In parallel, the Temporal Scaling Attention (TSA) introduces a learnable scaling factor to normalize temporal distances, ensuring frame partition invariance and consistent velocity estimation across different frame rates. These two modules are complementary: temporal scaling normalizes time intervals prior to Gaussian estimation, while Gaussian modeling enhances robustness to irregular distributions. Our experiments on mainstream benchmarks MSR-Action3D (+6.62% accuracy), NTU RGBD (+1.4% accuracy), and Synthia4D (+1.8% mIoU) demonstrate significant performance gains, offering a more efficient and principled paradigm for invariant 4D point cloud video understanding with superior accuracy, robustness, and scalability compared to Transformer based counterparts.

Jiayi Tian, Jiaze Wang

State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · Harbin Institute of Technology, Shenzhen, Pengcheng Laboratory

Point Cloud Learning Invariant Representation Learning Temporal Attention

Mar 17, 2026

Collaborative Temporal Feature Generation via Critic-Free Reinforcement Learning for Cross-User Sensor-Based Activity Recognition

Human Activity Recognition using wearable inertial sensors is foundational to healthcare monitoring, fitness analytics, and context-aware computing, yet its deployment is hindered by cross-user variability arising from heterogeneous physiological traits, motor habits, and sensor placements. Existing domain generalization approaches either neglect temporal dependencies in sensor streams or depend on impractical target-domain annotations. We propose a different paradigm: modeling generalizable feature extraction as a collaborative sequential generation process governed by reinforcement learning. Our framework, CTFG (Collaborative Temporal Feature Generation), employs a Transformer-based autoregressive generator that incrementally constructs feature token sequences, each conditioned on prior context and the encoded sensor input. The generator is optimized via Group-Relative Policy Optimization, a critic-free algorithm that evaluates each generated sequence against a cohort of alternatives sampled from the same input, deriving advantages through intra-group normalization rather than learned value estimation. This design eliminates the distribution-dependent bias inherent in critic-based methods and provides self-calibrating optimization signals that remain stable across heterogeneous user distributions. A tri-objective reward comprising class discrimination, cross-user invariance, and temporal fidelity jointly shapes the feature space to separate activities, align user distributions, and preserve fine-grained temporal content. Evaluations on the DSADS and PAMAP2 benchmarks demonstrate state-of-the-art cross-user accuracy (88.53% and 75.22%), substantial reduction in inter-task training variance, accelerated convergence, and robust generalization under varying action-space dimensionalities.

Xiaozhou Ye, Feng Jiang, Zihan Wang +3

School of Artificial Intelligence (School of Future Technology), Nanjing University of Information Science and Technology, Nanjing, China · School of Cyberspace Security, Nanjing University of Information Science and Technology, Nanjing, China · Jinling Hospital, Affiliated Hospital of Medical School, Nanjing University, Nanjing, China +1

Human Activity Recognition Domain Generalization Invariant Representation Learning RL for Generative Models

Mar 15, 2026

Make it SING: Analyzing Semantic Invariants in Classifiers

All classifiers, including state-of-the-art vision models, possess invariants, partially rooted in the geometry of their linear mappings. These invariants, which reside in the null-space of the classifier, induce equivalent sets of inputs that map to identical outputs. The semantic content of these invariants remains vague, as existing approaches struggle to provide human-interpretable information. To address this gap, we present Semantic Interpretation of the Null-space Geometry (SING), a method that constructs equivalent images, with respect to the network, and assigns semantic interpretations to the available variations. We use a mapping from network features to multi-modal vision language models. This allows us to obtain natural language descriptions and visual examples of the induced semantic shifts. SING can be applied to a single image, uncovering local invariants, or to sets of images, allowing a breadth of statistical analysis at the class and model levels. For example, our method reveals that ResNet50 leaks relevant semantic attributes to the null space, whereas DinoViT, a ViT pretrained with self-supervised DINO, is superior in maintaining class semantics across the invariant space.

Harel Yadid, Meir Yossef Levi, Roy Betser +1

Viterbi Faculty of Electrical and Computer Engineering, Technion – Israel Institute of Technology, Haifa, Israel

Explainable Image Classification Invariant Representation Learning

Mar 13, 2026

VIRD: View-Invariant Representation through Dual-Axis Transformation for Cross-View Pose Estimation

Accurate global localization is critical for autonomous driving and robotics, but GNSS-based approaches often degrade due to occlusion and multipath effects. As an emerging alternative, cross-view pose estimation predicts the 3-DoF camera pose corresponding to a ground-view image with respect to a geo-referenced satellite image. However, existing methods struggle to bridge the significant viewpoint gap between the ground and satellite views mainly due to limited spatial correspondences. We propose a novel cross-view pose estimation method that constructs view-invariant representations through dual-axis transformation (VIRD). VIRD first applies a polar transformation to the satellite view to facilitate horizontal correspondence, then uses context-enhanced positional attention on the ground and polar-transformed satellite features to mitigate vertical misalignment, explicitly bridging the viewpoint gap. To further strengthen view invariance, we introduce a view-reconstruction loss that encourages the derived representations to reconstruct the original and cross-view images. Experiments on the KITTI and VIGOR datasets demonstrate that VIRD outperforms the state-of-the-art methods without orientation priors, reducing median position and orientation errors by 50.7% and 76.5% on KITTI, and 18.0% and 46.8% on VIGOR, respectively.

Juhye Park, Wooju Lee, Dasol Hong +4

Urban Robotics Lab, School of Electrical Engineering, KAIST · Hanwha Aerospace

Cross-View Geo-Localization Invariant Representation Learning

Mar 13, 2026

Text-Phase Synergy Network with Dual Priors for Unsupervised Cross-Domain Image Retrieval

This paper studies unsupervised cross-domain image retrieval (UCDIR), which aims to retrieve images of the same category across different domains without relying on labeled data. Existing methods typically utilize pseudo-labels, derived from clustering algorithms, as supervisory signals for intra-domain representation learning and cross-domain feature alignment. However, these discrete pseudo-labels often fail to provide accurate and comprehensive semantic guidance. Moreover, the alignment process frequently overlooks the entanglement between domain-specific and semantic information, leading to semantic degradation in the learned representations and ultimately impairing retrieval performance. This paper addresses the limitations by proposing a Text-Phase Synergy Network with Dual Priors(TPSNet). Specifically, we first employ CLIP to generate a set of class-specific prompts per domain, termed as domain prompt, serving as a text prior that offers more precise semantic supervision. In parallel, we further introduce a phase prior, represented by domain-invariant phase features, which is integrated into the original image representations to bridge the domain distribution gaps while preserving semantic integrity. Leveraging the synergy of these dual priors, TPSNet significantly outperforms state-of-the-art methods on UCDIR benchmarks.

Jing Yang, Hui Xue, Shipeng Zhu +1

School of Computer Science and Engineering, Southeast University, China · Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China

Unsupervised Representation Learning Invariant Representation Learning Cross-Modal Alignment

Mar 8, 2026

Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group

G

acts transitively on a space

M

, any

G

-invariant function on a product space

X \times M

can be reduced to an invariant of the isotropy subgroup

H

of

M

acting on

X

alone. Our approach establishes an explicit orbit equivalence

(X \times M)/G \cong X/H

, yielding a principled reduction that preserves expressivity. We apply this characterization to Equivariant Neural Fields, extending them to arbitrary group actions and homogeneous conditioning spaces, and thereby removing the major structural constraints imposed by existing methods.

Alejandro García-Castellanos, Gijs Bellaard, Remco Duits +2

Amsterdam Machine Learning Lab (AMLab), University of Amsterdam · Department of Mathematics and Computer Science, Eindhoven University of Technology · Leiden Institute of Advanced Computer Science, Universiteit Leiden

Equivariant Neural Networks Invariant Representation Learning

Mar 7, 2026

Learning Clinical Representations Under Systematic Distribution Shift

Clinical machine learning models are increasingly trained using large scale, multimodal foundation paradigms, yet deployment environments often differ systematically from the data generating settings used during training. Such shifts arise from heterogeneous measurement policies, documentation practices, and institutional workflows, leading to representation entanglement between physiologic signal and practice specific artifacts. In this work, we propose a practice invariant representation learning framework for multimodal clinical prediction. We model clinical observations as arising from latent physiologic factors and environment dependent processes, and introduce an objective that jointly optimizes predictive performance while suppressing environment predictive information in the learned embedding. Concretely, we combine supervised risk minimization with adversarial environment regularization and invariant risk penalties across hospitals. Across multiple longitudinal EHR prediction tasks and cross institution evaluations, our method improves out of distribution AUROC by up to 2 to 3 points relative to masked pretraining and standard supervised baselines, while maintaining in distribution performance and improving calibration. These results demonstrate that explicitly accounting for systematic distribution shift during representation learning yields more robust and transferable clinical models, highlighting the importance of structural invariance alongside architectural scale in healthcare AI.

Yuanyun Zhang, Shi Li

Columbia University

OOD Generalization Invariant Representation Learning Adversarial Representation Learning Clinical Risk Prediction Longitudinal EHR Modeling

Mar 7, 2026

VINO: Video-driven Invariance for Non-contextual Objects via Structural Prior Guided De-contextualization

Self-supervised learning (SSL) has made rapid progress, yet learned features often over-rely on contextual shortcuts-background textures and co-occurrence statistics. While video provides rich temporal variation, dense in-the-wild streams with strong ego-motion create a co-occurrence trap: foreground objects and background context move coherently, encouraging representations to collapse into scene encoders. To address this, we propose VINO (Video-driven Invariance for Non-Contextual Objects), a teacher-student framework that learns robust image encoders from dense video by imposing a structural information bottleneck. Using a class-agnostic structural prior solely to generate views-not as semantic pseudo-labels-VINO forms an asymmetric distillation problem. The teacher predicts from a foreground-union view with the background suppressed, while the student observes object-conditioned scene views that retain surrounding context but remove competing instances. Matching these targets via masked distillation makes background cues unreliable, pushing the representation toward object-centric invariances. We further enforce temporal object permanence via teacher-anchored cross-time distillation over track-matched objects, and stabilize part-to-whole consistency with mask-guided local views. Through attention visualization and unsupervised object discovery on PASCAL VOC, we demonstrate that VINO effectively disentangles foreground from background. Pretrained on the dense Walking Tours Venice video, VINO achieves 34.8 CorLoc, yielding highly focused, shape-biased representations that substantially outperform prior dense-video and motion-guided SSL baselines.

Seul-Ki Yeom, Marcel Simon, Eunbin Lee +1

Nota AI GmbH

Self-Supervised Visual Representation Learning Object-Centric Representation Learning Video Object-Centric Learning Invariant Representation Learning Video Representation Learning

Mar 5, 2026

TransMASK: Masked State Representation through Learned Transformation

When humans learn new manipulation skills, they are able to generalize these skills to new contexts and environments. In particular, when learning, humans can easily separate task-relevant aspects of the environment (e.g., object location) and distractors (e.g., the table color). Ideally, robot policies should be able to learn similar, generalizable representations, but instead they often fail under small environment shifts such as changes in lighting, object instance, or initial configuration. In this paper, we propose a self-supervised method that learns a mask which, when multiplied by the observed image features, attempts to transform these features to retain only those which are relevant to the task. Our method --- which we call TransMASK --- can be combined with a variety of imitation learning frameworks (such as diffusion policies) without any additional labels or alterations to the loss function. By introducing a learned mask to the network during training, we aim to induce competitive pressure among the image features during training to force the policy to only attend to features which are consistently task-relevant. We find empirically that our masks are interpretable and can reject known spurious features such as the position of distractor objects or the background color. When compared to other representation learning methods for imitation learning, we find that TransMASK results in policies that are more robust to distribution shifts for irrelevant features, achieving at least 30 % improvement over the baselines when tested on out-of-distribution environments. See our project website: https://transmask.github.io/TransMASK/

Sagar Parekh, Preston Culbertson, Dylan P. Losey

Mechanical Engineering Department, Virginia Tech · Computer Science Department, Cornell University

Representation Learning Robot Imitation Learning Invariant Representation Learning Self-Supervised Visual Representation Learning

Mar 5, 2026

Embedded Inter-Subject Variability in Adversarial Learning for Inertial Sensor-Based Human Activity Recognition

This paper addresses the problem of Human Activity Recognition (HAR) using data from wearable inertial sensors. An important challenge in HAR is the model's generalization capabilities to new unseen individuals due to inter-subject variability, i.e., the same activity is performed differently by different individuals. To address this problem, we propose a novel deep adversarial framework that integrates the concept of inter-subject variability in the adversarial task, thereby encouraging subject-invariant feature representations and enhancing the classification performance in the HAR problem. Our approach outperforms previous methods in three well-established HAR datasets using a leave-one-subject-out (LOSO) cross-validation. Further results indicate that our proposed adversarial task effectively reduces inter-subject variability among different users in the feature space, and it outperforms adversarial tasks from previous works when integrated into our framework. Code: https://github.com/FranciscoCalatrava/EmbeddedSubjectVariability.git

Francisco M. Calatrava-Nicolás, Shoko Miyauchi, Vitor Fortes Rey +3

Centre for Applied Autonomous Sensor Systems (AASS), Örebro University, Örebro, Sweden · Faculty of Information Science & Electrical Engineering, Kyushu University, Fukuoka, Japan · RPTU, Kaiserslautern, Germany +2

Human Activity Recognition Domain-Adversarial Learning Invariant Representation Learning

Mar 4, 2026

Soft Equivariance Regularization for Invariant Self-Supervised Learning

Self-supervised learning (SSL) typically learns representations invariant to semantic-preserving augmentations. While effective for recognition, enforcing strong invariance can suppress transformation-dependent structure that is useful for robustness to geometric perturbations and spatially sensitive transfer. A growing body of work, therefore, augments invariance-based SSL with equivariance objectives, but these objectives are often imposed on the same final representation. We empirically observe a trade-off in this coupled setting: pushing equivariance regularization toward deeper layers improves equivariance scores but degrades ImageNet-1k linear evaluation, motivating a layer-decoupled design. Motivated by this trade-off, we propose Soft Equivariance Regularization (SER), a plug-in regularizer that decouples where invariance and equivariance are enforced: we keep the base SSL objective unchanged on the final embedding, while softly encouraging equivariance on an intermediate spatial token map via analytically specified group actions

ρ_g

applied directly in feature space. SER learns/predicts no per-sample transformation codes/labels, requires no auxiliary transformation-prediction head, and adds only 1.008x training FLOPs. On ImageNet-1k ViT-S/16 pretraining, SER improves MoCo-v3 by +0.84 Top-1 in linear evaluation under a strictly matched 2-view setting and consistently improves DINO and Barlow Twins; under matched view counts, SER achieves the best ImageNet-1k linear-eval Top-1 among the compared invariance+equivariance add-ons. SER further improves ImageNet-C/P by +1.11/+1.22 Top-1 and frozen-backbone COCO detection by +1.7 mAP. Finally, applying the same layer-decoupling recipe to existing invariance+equivariance baselinesimproves their accuracy, suggesting layer decoupling as a general design principle for combining invariance and equivariance.

Joohyung Lee, Changhun Kim, Hyunsu Kim +2

AITRICS · Voronoi Inc. · Korea Advanced Institute of Science and Technology (KAIST)

Self-Supervised Visual Representation Learning Equivariant Representation Learning Invariant Representation Learning Equivariant Neural Networks

Mar 3, 2026

Coalgebras for categorical deep learning: Representability and universal approximation

Categorical deep learning (CDL) has recently emerged as a framework that leverages category theory to unify diverse neural architectures. While geometric deep learning (GDL) is grounded in the specific context of invariants of group actions, CDL aims to provide domain-independent abstractions for reasoning about models and their properties. In this paper, we contribute to this program by developing a coalgebraic foundation for equivariant representation in deep learning, as classical notions of group actions and equivariant maps are naturally generalized by the coalgebraic formalism. Our first main result demonstrates that, given an embedding of data sets formalized as a functor from SET to VECT, and given a notion of invariant behavior on data sets modeled by an endofunctor on SET, there is a corresponding endofunctor on VECT that is compatible with the embedding in the sense that this lifted functor recovers the analogous notion of invariant behavior on the embedded data. Building on this foundation, we then establish a universal approximation theorem for equivariant maps in this generalized setting. We show that continuous equivariant functions can be approximated within our coalgebraic framework for a broad class of symmetries. This work thus provides a categorical bridge between the abstract specification of invariant behavior and its concrete realization in neural architectures.

Dragan Mašulović

University of Novi Sad, Faculty of Sciences Department of Mathematics and Informatics Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia

Equivariant Representation Learning Invariant Representation Learning Neural Network Approximation Theory Category Theory

Mar 2, 2026

MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentials

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (Materials Representation and Interaction Simulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity

O(N)

, enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.

Yuanchang Zhou, Siyu Hu, Xiangyu Zhang +3

State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences · School of Advanced Interdisciplinary Sciences, UCAS

Machine Learning Interatomic Potentials Computational Materials Science Invariant Representation Learning Materials Property Prediction

Feb 27, 2026

FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting

Learning directly from boundary representations (B-reps) has significantly advanced 3D CAD analysis. However, state-of-the-art B-rep learning methods rely on absolute coordinates and normals to encode global context, making them highly sensitive to rotations. Our experiments reveal that models achieving over 95% accuracy on aligned benchmarks can collapse to as low as 10% under arbitrary

\mathbf{SO}(3)

rotations. To address this, we introduce FoV-Net, the first B-rep learning framework that captures both local surface geometry and global structural context in a rotation-invariant manner. Each face is represented by a Local Reference Frame (LRF) UV-grid that encodes its local surface geometry, and by Field-of-View (FoV) grids that capture the surrounding 3D context by casting rays and recording intersections with neighboring faces. Lightweight CNNs extract per-face features, which are propagated over the B-rep graph using a graph attention network. FoV-Net achieves state-of-the-art performance on B-rep classification and segmentation benchmarks, demonstrating robustness to arbitrary rotations while also requiring less training data to achieve strong results.

Matteo Ballegeer, Dries F. Benoit

Boundary Representation Modeling 3D Representation Learning Invariant Representation Learning

Feb 26, 2026

Learning Continuous Wasserstein Barycenter Space for Generalized All-in-One Image Restoration

Despite substantial advances in all-in-one image restoration for addressing diverse degradations within a unified model, existing methods remain vulnerable to out-of-distribution degradations, thereby limiting their generalization in real-world scenarios. To tackle the challenge, this work is motivated by the intuition that multisource degraded feature distributions are induced by different degradation-specific shifts from an underlying degradation-agnostic distribution, and recovering such a shared distribution is thus crucial for achieving generalization across degradations. With this insight, we propose BaryIR, a representation learning framework that aligns multisource degraded features in the Wasserstein barycenter (WB) space, which models a degradation-agnostic distribution by minimizing the average of Wasserstein distances to multisource degraded distributions. We further introduce residual subspaces, whose embeddings are mutually contrasted while remaining orthogonal to the WB embeddings. Consequently, BaryIR explicitly decouples two orthogonal spaces: a WB space that encodes the degradation-agnostic invariant contents shared across degradations, and residual subspaces that adaptively preserve the degradation-specific knowledge. This disentanglement mitigates overfitting to in-distribution degradations and enables adaptive restoration grounded on the degradation-agnostic shared invariance. Extensive experiments demonstrate that BaryIR performs competitively against state-of-the-art all-in-one methods. Notably, BaryIR generalizes well to unseen degradations (e.g., types and levels) and shows remarkable robustness in learning generalized features, even when trained on limited degradation types and evaluated on real-world data with mixed degradations.

Xiaole Tang, Xiaoyi He, Jiayi Xu +2

School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi, P.R. China.

All-in-One Image Restoration OOD Generalization Invariant Representation Learning

Feb 26, 2026

SO3UFormer: Learning Intrinsic Spherical Features for Rotation-Robust Panoramic Dense Prediction

Panoramic dense-prediction models, spanning semantic segmentation and depth estimation, are typically trained under a strict gravity-aligned assumption. Real-world captures, however, routinely violate it: handheld devices jitter and aerial platforms change attitude, so the camera is rarely upright. Under such 3D reorientation, standard spherical Transformers overfit global latitude cues and collapse. We introduce SO3UFormer, an architecture that learns intrinsic spherical features largely decoupled from the underlying coordinate frame, through three geometric components: (1) removing absolute latitude encoding, which breaks the dependence on the gravity axis; (2) quadrature-consistent spherical attention, which corrects for non-uniform sampling density; and (3) a gauge-aware relative positional bias built from local tangent-plane angles rather than global axes. A logit-space SO(3)-consistency regularizer, used only during training, further suppresses residual discretization effects. To benchmark robustness, we introduce Pose35, a variant of Stanford2D3D perturbed by random rotations within

\pm 35^\circ

, and evaluate under a full, arbitrary SO(3) stress test. There, the baseline SphereUFormer collapses from 67.53 mIoU on Pose35 to 25.26 under the full SO(3) test, whereas SO3UFormer reaches 72.03 on Pose35 and retains 70.67 under the same test. Similarly, on a second real-world dataset (Matterport3D) for segmentation and on panoramic depth estimation, SO3UFormer remains essentially rotation-invariant while the gravity-anchored baseline again loses most of its accuracy. Code and models are available at https://github.com/zhuqinfeng1999/SO3UFormer.

Qinfeng Zhu, Yunxi Jiang, Lei Fan

University of Liverpool, United Kingdom. · CNRS, France. · Xi’an Jiaotong-Liverpool University, China.

Depth Estimation Vision Transformer Invariant Representation Learning Semantic Segmentation Panoramic Depth Estimation

Feb 26, 2026

Transformers converge to invariant algorithmic cores

Training selects for behavior, not circuitry: many weight configurations can implement the same function. Studying any single trained neural network thus risks describing accidents of one training run rather than the computation itself. This work shifts focus from what transformers happen to do to what they must do by extracting algorithmic cores, compact subspaces that are necessary and sufficient for a task and that recur across independently trained models. Here, Algorithmic Core Extraction (ACE) is introduced to isolate these subspaces, causally validate them, and recover the algorithms they implement across settings ranging from synthetic tasks to large-scale pretrained models. Markov-chain transformers embed three-dimensional cores in nearly orthogonal subspaces yet recover identical transition spectra. Modular-addition transformers form compact cyclic cores at grokking that later inflate under continued regularization, redundantly distributing the same computation across many functionally equivalent modes. This functional redundancy is found to accelerate the transition from memorization to generalization, yielding an inverse scaling law for grokking time. In six language models spanning more than two orders of magnitude in scale (GPT-2 Small/Medium/Large, LLaMA-3.1, Gemma-2, and Qwen2.5), subject-verb agreement is governed by a single, steerable axis that aligns across architectures. Flipping this axis inverts grammatical number throughout open-ended generation. Together these results suggest that beneath the apparent complexity of trained transformers lies a simpler, shared computational structure, and that targeting invariants rather than parameterizations may offer a more tractable path to mechanistic understanding and control. Code: https://github.com/joshseth/cores

Joshua S. Schiffman

New York Genome Center, New York, NY, USA.

Transformer Interpretability Invariant Representation Learning Grokking

Feb 24, 2026

Assessing the Impact of Speaker Identity in Speech Spoofing Detection

Spoofing detection systems are typically trained using diverse recordings from multiple speakers, often assuming that the resulting embeddings are independent of speaker identity. However, this assumption remains unverified. In this paper, we investigate the impact of speaker information on spoofing detection systems. We propose two approaches within our Speaker-Invariant Multi-Task framework, one that models speaker identity within the embeddings and another that removes it. SInMT integrates multi-task learning for joint speaker recognition and spoofing detection, incorporating a gradient reversal layer. Evaluated using four datasets, our speaker-invariant model reduces the average equal error rate by 17% compared to the baseline, with up to 48% reduction for the most challenging attacks (e.g., A11).

Anh-Tuan Dao, Driss Matrouf, Nicholas Evans

Laboratoire d’informatique d’Avignon, France · EURECOM, Sophia Antipolis, France

Audio Deepfake Detection Invariant Representation Learning

Feb 23, 2026

Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning

Mendelian Randomization (MR) is a prominent observational epidemiological research method designed to address unobserved confounding when estimating causal effects. However, core assumptions -- particularly the independence between instruments and unobserved confounders -- are often violated due to population stratification or assortative mating. Leveraging the increasing availability of multi-environment data, we propose a representation learning framework that exploits cross-environment invariance to recover latent exogenous components of genetic instruments. We provide theoretical guarantees for identifying these latent instruments under various mixing mechanisms and demonstrate the effectiveness of our approach through simulations and semi-synthetic experiments using data from the All of Us Research Hub.

Shimeng Huang, Matthew Robinson, Francesco Locatello

Institute of Science and Technology Austria (ISTA)

Instrumental Variable Estimation Causal Identifiability Invariant Representation Learning

Feb 21, 2026

Toward Manifest Relationality in Transformers via Symmetry Reduction

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly breaking symmetry, we propose a complementary framework based on symmetry reduction. We reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction. This perspective yields architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.

J. François, L. Ravera

Mons University (UMONS), 20 Place du Parc, 7000 Mons, Belgium. · Grupo de Investigación en Física Teórica, Universidad Católica De La Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile.

Transformer Transformer Attention Invariant Representation Learning Neural Representation Geometry