Orthogonal Representation Learning

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1 paper in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

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Latest papers 21

Oct 7, 2026cs.CV

LoomSC: Scalable Deep Subspace Clustering with Projector Factorization and Exact Spectral Reduction

Dense self-expression matrices and full-affinity spectral clustering limit the scalability of subspace clustering. We introduce the Latent Orthogonal Optimization Model for Subspace Clustering (LoomSC), a framework that addresses both bottlenecks through projector factorization and exact spectral reduction. Motivated by the spectral structure of least-squares regression, LoomSC jointly learns latent features and a projector self-representation through two thin factors. Alternating Procrustes and least-squares updates preserve the sample factor's orthogonality while keeping the coefficient matrix implicit. We construct a nonnegative quadratic affinity that preserves the projector's support. An exact feature map then reduces its normalized spectral problem to an eigenproblem whose dimension depends only on the factor width. Neither the full affinity nor the sample Laplacian needs to be formed. Our analysis quantifies the projector approximation and identifies conditions for subspace preservation and within-subspace connectivity. For fixed dimensions and iteration budgets, the complete pipeline has linear time and memory complexity in the number of samples. Across five image-clustering benchmarks, LoomSC ranks first or second in all 15 dataset-metric comparisons against 9 state-of-the-art baselines. Its mean accuracy exceeds the highest baseline mean by 6.66 percentage points. Synthetic experiments scale to 500,000 samples while maintaining at least 99.8% accuracy.

Nairouz Mrabah, Youssef Melki, Mohamed Bouguessa +3

École de technologie supérieure (ÉTS), Montréal, QC, Canada · University of Bahrain (UOB), Kingdom of Bahrain · Université du Québec à Montréal (UQAM), Montréal, QC, Canada +1

Clustering Spectral Clustering Deep Clustering Image Clustering Orthogonal Representation Learning

Sep 11, 2026cs.LG

Learning Orthogonal Multi-Index Models Beyond Small Initialization: Incremental Learning, Competitive Dynamics and Symmetry

Recent work has identified incremental learning in shallow networks trained on single-index and multi-index models. However, existing analyses often rely on simplifying settings, such as small initialization, correlation loss, or layer-wise training. These choices reduce neuron interactions and leave some feature learning dynamics under standard initialization unexplored. We study training dynamics for polynomial-width two-layer networks learning orthogonal multi-index targets under standard initialization using polynomially many samples. We first prove that incremental learning still occurs: the loss decreases sequentially according to the Hermite expansion of the target, with lower-order components learned before higher-order components recover the individual target directions. In this standard initialization regime, training also shows a competitive reallocation of parameter mass: after the total mass fits the target mean and stabilizes, mass shifts into the target subspace and then concentrates on aligned neurons. Our theoretical analysis uses slightly modified gradient flow, while vanilla gradient descent empirically exhibits the same qualitative dynamics. Technically, we introduce a symmetry-based finite-width approximation via symmetrized networks, rather than comparing directly with an infinite-width limit. This yields better control of approximation errors and may be of independent interest.

Mo Zhou, Weihang Xu, Simon S. Du +1

University of Washington · Amazon, Inc.

Shallow Neural Networks Orthogonal Representation Learning Incremental Learning Neural Network Training Dynamics Multi-Index Models

Aug 20, 2026cs.LG

Orthogonal JEPA: Factorized Predictive States for Latent World Models

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Taoyong Cui, Pheng Ann Heng, Wanli Ouyang

The Chinese University of Hong Kong (CUHK)

Joint-Embedding Predictive Architecture Orthogonal Representation Learning Predictive Representation Learning Latent World Models

Aug 13, 2026cs.LG

Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration

We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.

Sabin Roman, Ljupco Todorovski, Saso Dzeroski

Department of Knowledge Technologies, Jožef Stefan Institute · Faculty of Mathematics and Physics, University of Ljubljana

Sparse Identification of Nonlinear Dynamics Nonlinear System Identification Orthogonal Representation Learning ODE Discovery

Aug 12, 2026cs.LG

Exploring Oversmoothing with Householder Matrices

Deep graph neural networks(GNNs) suffer from oversmoothing- a progressive collapse of node representation towards a low information subspace as network depth increases because the normalized graph propagation operator is repeatedly applied directly to the hidden representations. In this work we study Householder Graph Neural Network (HouseGNN). Rather than updating the hidden state like standard GCN, HouseGNN uses the aggregated neighbourhood message solely to estimate a reflection direction; the node embedding is then updated by a Householder reflector followed by GroupSort, yielding a piecewise orthogonal layer that preserves Euclidean norm at every node and at every depth. We prove three core properties: (i) every internal layer preserves the node-wise Euclidean norm; (ii) the Householder reflector is scale scale and sign-invariant in the message; and (iii) pairwise distance between nodes can change through mismatch between node-wise orthogonal operators.

Bhaskar Karol

Graph Neural Networks Orthogonal Representation Learning

Jul 31, 2026cs.SE

OrEdge: Efficient Multi-Modal Anomaly Detection in Distributed Software Systems via Orthogonal-Domain Learning

We introduce Orthogonal-Edge (OrEdge), a lightweight framework for real-time anomaly detection in multi-modal distributed software systems. Unlike existing approaches that rely on computationally expensive attention- and graph-based architectures, OrEdge leverages orthogonal-domain temporal representations to achieve accurate anomaly detection with substantially lower computational complexity and model size. It jointly analyzes heterogeneous monitoring data, including logs, metrics, and traces, to identify abnormal software behavior, capture temporal dependencies, and reduce redundancy across observability signals. At its core, OrEdge incorporates OrEdgeCore, a lightweight orthogonal-domain reconstruction module that captures recurring temporal patterns while suppressing transient variations. Evaluated on three real-world microservice datasets (MSDS, SN, and TT), OrEdge achieves competitive detection performance while reducing the reconstruction model size to at most 9.6K parameters, compared with 20K--143K parameters in existing methods. This compact design enables efficient deployment on resource-constrained edge devices: on Raspberry Pi platforms, OrEdge achieves sub-second inference and reduces inference latency by over an order of magnitude compared with existing approaches. Extensive ablation studies, sensitivity analyses, orthogonal basis evaluations, and qualitative case studies further validate the effectiveness of each design component. Overall, OrEdge demonstrates that orthogonal-domain temporal modeling provides an effective alternative to computationally intensive attention- and graph-based architectures, achieving a favorable balance between detection accuracy and computational efficiency for real-time multi-modal anomaly detection in edge environments. The code is available at https://github.com/theamrzaki/MicroService_Twin_Original.

Amr M. Zaki, Farhoud Jafari Kaleibar, Honggeun Ji +2

School of Engineering, York University, Toronto, ON, Canada.

Edge Inference Orthogonal Representation Learning Reconstruction-Based Anomaly Detection Multimodal Anomaly Detection Anomaly Detection

Jul 24, 2026cs.CV

Projection Pursuit CPCANet for Domain Generalization

Domain Generalization (DG) aims to learn representations robust to distribution shifts. Recent geometric alignment methods, such as CPCANet, extract domain-invariant structures through batch-wise Common Principal Component Analysis (CPCA). However, CPCANet suffers from rank-deficient covariance estimation due to the small-sample-size issue in mini-batch training. To address this limitation, we propose Projection Pursuit CPCANet (PP-CPCANet), a covariance-free framework that learns a global orthogonal basis on the Stiefel manifold and jointly optimizes it with network parameters via the Cayley transform. We further introduce a symmetry-breaking detached-median PP dispersion objective to extract common principal components (CPCs) with dense and robust optimization signals. Experiments on four DG benchmarks show that PP-CPCANet achieves SOTA performance while maintaining stable training.

Yu-Hsi Chen, Abd-Krim Seghouane

The University of Melbourne

Principal Component Analysis Domain Generalization Orthogonal Representation Learning Cross-Domain Generalization

Jul 24, 2026cs.CV

Gradient-Based Latent Decomposition Reveals Mechanisms of Feature Degradation in Weakly Supervised Mammography

Weakly supervised hierarchical models exhibit a persistent asymmetry: coarse lesion-type features are preserved under reconstruction while fine-grained malignancy cues degrade---a pattern with direct consequences for the clinical reliability of breast cancer screening pipelines. We introduce gradient-based orthogonal latent decomposition for hierarchical Variational Autoencoders~(H-VAEs) to mechanistically explain this asymmetry. The latent space is partitioned into a task-aligned component~(

z_1

), shaped by coarse supervisory gradients, and an orthogonal residual~(

z_{\text{res}}

) capturing remaining representational capacity. On~~3,550 mammographic Regions of Interest~~(ROIs) from CBIS-DDSM, only~

\sim

4.4% of latent magnitude aligns with supervisory gradients, leaving~

\sim

95.6% in the orthogonal residual upon which fine-grained pathology prediction primarily depends. The model achieves Stage-1~~AUC~~0.866 and Stage 2~~AUC~~0.552, with a reconstruction stability gap of

Δ_{\text{diag}}=5\%

(

p=0.005

) and a classification gap of

Δ_{\text{AUC}}=0.314

(

p{<}0.001

). Latent ablation confirms that features for both tasks reside heavily in~

z_{\text{res}}

, structurally explaining why reconstruction degrades pathology stability disproportionately. Comparisons with Multi-Instance Learning~(MIL) and Multi-Task Learning~(MTL) confirm generalization across architectures and modalities. These findings reveal that in high-dimensional spaces, a single coarse supervisory signal isolates only a sparse 1D latent direction, forcing critical fine-grained features into the vulnerable residual subspace.

Vinceline Bertrand, Ionut Cardei

Florida Atlantic University, Boca Raton, FL, USA

Variational Autoencoders Hierarchical Representation Learning Orthogonal Representation Learning Medical Image Classification Weakly Supervised Learning Mammography

Jul 7, 2026cs.SD

Escaping the Procrustean Bed: Groupwise Orthogonal Connectors for Audio-Language Models

Audio-language models compress a speech encoder's output through a Querying Transformer (Q-Former) connector before feeding it to a large language model. We identify two failures in this compression. The connector's output vectors collapse to a single direction, and different speakers produce nearly indistinguishable outputs, with paralinguistic cues such as speaker identity, gender, and prosody lost along the way. Our method, ORCA, reverses this collapse by splitting the queries into groups whose outputs are constrained to point in different directions. On SAKURA multi-hop reasoning, ORCA gains 26.4 points over an identically trained 4B baseline, reaching 75.2% (vs. 49.0% for the 8B Audio Flamingo-3). At the connector level, the same change cuts query redundancy by 12x and raises cross-speaker variance by 75x.

Ho-Lam Chung, Ke-Han Lu, Yi-Cheng Lin +3

Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan · ASUS AICS, Taipei, Taiwan

Audio Representation Learning Representation Learning Representation Collapse Orthogonal Representation Learning Audio-Language Models

Jul 6, 2026cs.LG

Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spaces

Principal Component Analysis or PCA-like properties (orthogonality, variance ranking) are seldom realized in deep autoencoder architectures. In this work, we present ODIN (Orthogonal Dendritic Intrinsic Network), a novel autoencoder architecture that recovers PCA-like latent structure in a fully non-linear regime. By incorporating a set of geometric constraints directly into the training objective, ODIN encourages latent dimensions to be mutually orthogonal and ordered by explained variance, mirroring the interpretable decomposition of PCA while retaining the expressive power of deep networks. We provide theoretical grounding for these constraints and demonstrate their compatibility with standard encoder-decoder frameworks. We also establish empirical results for both synthetic and real world datasets, establishing a principled path toward interpretable, structured feature learning and dimensionality reduction.

Jeanie Schreiber, Tyrus Berry, Zeeshan Ahmed

Department of Mathematical Sciences George Mason University Fairfax, VA 22030, USA · Sensor Science Division, Physical Measurement Laboratory NIST Gaithersburg, MD 20899, USA

Representation Learning Principal Component Analysis Autoencoders Unsupervised Representation Learning Orthogonal Representation Learning Dimensionality Reduction+1

Jun 19, 2026cs.LG

Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability

This paper explores unsupervised disentangled representation learning from a functional perspective. We define latent concepts as factors that influence observations through locally orthogonal directions, formalized as an orthogonality constraint on the Jacobian of the generative mapping. We prove that this condition yields identifiability of general nonlinear generative models, without requiring statistical independence or causal assumptions, provided the latent domain admits all combinations of factor values. Experiments with orthogonality-regularized normalizing flows empirically confirm the theory, demonstrate reliable recovery of ground-truth factors, and shed light on the success of VAEs. These findings challenge the prevailing impossibility claims for unsupervised disentanglement and provide a principled alternative foundation.

Mathieu Cyrille Simon, Pascal Frossard, Christophe De Vleeschouwer

1UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium · 2EPFL, LTS4 laboratory, Lausanne, Switzerland.

Unsupervised Learning Disentangled Representation Learning Latent Variable Models Representation Identifiability Orthogonal Representation Learning

Jun 15, 2026cs.SD

Dual-Granularity Orthogonal Disentanglement for Generalizable Audio Deepfake Detection

Audio deepfake detectors often fail to generalize across speakers, as they learn speaker-identity features rather than synthesis artifacts, known as implicit identity leakage. Existing methods address this but incur architectural complexity or training instability. This paper proposes a dual-granularity orthogonal disentanglement framework enforcing feature independence at two levels: sample-level cosine orthogonality captures directional decorrelation, while batch-level cross-covariance regularization eliminates linear correlations across embedding dimensions. A curriculum disentanglement schedule progressively strengthens the orthogonality constraint without auxiliary networks or adversarial dynamics. Experiments on ASVspoof 2019 LA, ASVspoof 2021 DF, and In-the-Wild datasets demonstrate that the proposed method achieves 1.35%, 7.88%, and 21.58% equal error rates (EER), respectively, surpassing gradient reversal disentanglement by 2.60% absolute on cross-dataset transfer.

Zhuodong Liu, Hugen Lv, Xiangyu Li +1

Beijing Jiaotong University, China · Shanghai Jiao Tong University, China · ITMO University, Russia

Representation Learning Audio Deepfake Detection Domain Generalization Orthogonal Representation Learning Speaker Disentanglement

May 29, 2026cs.CV

OSCS-SupCon: Orthogonal Sigmoid-based Common and Style Supervised Contrastive Learning for Robust Feature Disentanglement

Supervised Contrastive Learning (SupCon) has achieved strong performance by explicitly modeling pairwise relationships among samples. However, existing SupCon-based methods suffer from two key limitations: negative-sample dilution induced by the standard InfoNCE loss, and feature-space entanglement caused by the lack of explicit constraints separating category-relevant (common) and category-irrelevant (style) features. These limitations reduce feature discriminability and generalization ability. To address these issues, we propose OSCS-SupCon (Orthogonal Sigmoid-based Common and Style Supervised Contrastive Learning), a unified framework that combines a sigmoid-based pairwise contrastive objective with explicit orthogonality constraints. Specifically, we introduce a sigmoid-based contrastive loss with two learnable parameters, temperature and bias, which adaptively modulate pairwise decision boundaries and alleviate negative-sample dilution. Furthermore, we enforce orthogonality between common and style feature subspaces via a linear projection with ReLU nonlinearity, thereby reducing feature overlap and improving disentanglement of style-irrelevant representations. Extensive experiments on six benchmark datasets demonstrate that OSCS-SupCon consistently outperforms state-of-the-art supervised contrastive learning methods across multiple backbone architectures. In particular, on the fine-grained CUB200-2011 dataset with a ResNet-18 backbone, the proposed method achieves a 3.4% improvement in classification accuracy over CS-SupCon, highlighting its robustness and generalization capability. Ablation studies further confirm the effectiveness of each component.

Bin Wang, Fadi Dornaika

University B.of theWang1Basqueand Country · IKERBASQUE,2

Contrastive Learning Disentangled Representation Learning Representation Learning Orthogonal Representation Learning Supervised Contrastive Learning

May 25, 2026cs.LG

Learning in Low-Dimensional Subspaces: Orthogonal Bottlenecks for Reinforcement Learning

Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple yet effective representation-level prior that inserts a fixed orthonormal projection to constrain encoder features to a low-dimensional subspace, requiring no auxiliary objectives, pretraining, or changes to the underlying RL algorithm. Under a linear realizability assumption, we prove that when the bottleneck dimension exceeds the intrinsic rank of the optimal value function in feature space, the bottleneck preserves expressivity and leaves the induced gradient dynamics unchanged up to an equivalent low-dimensional parameterization. Empirically, we find that across both single and multi-task benchmarks, baseline performance is either matched or improved once the bottleneck dimension exceeds a small task-dependent threshold; in many cases, value representations can be compressed to extremely low dimensions without loss, and the minimal sufficient dimension depends far more on environment complexity than encoder width. In addition, we analyze representation geometry and find that orthogonal bottlenecks stabilize feature norms and are associated with higher effective rank. Together, these results support a representation-space interpretation of the manifold hypothesis in reinforcement learning and position orthogonal bottlenecks as a lightweight, architecture-agnostic mechanism for shaping RL representations.

Aleksandar Todorov, Matthia Sabatelli

University of Groningen, Groningen, The Netherlands

Representation Learning Reinforcement Learning Information Bottleneck Orthogonal Representation Learning Representation Learning for RL State Representation Learning

May 18, 2026cs.LG

AURORA: Contextual Orthogonalization for Geometric Representation Learning in Healthcare Foundation Models

Recent healthcare foundation models have achieved strong predictive performance through large scale self supervised learning, yet their latent representations frequently entangle physiologic severity, intervention intensity, observational structure, and institutional workflow into shared embedding directions. While effective for downstream prediction, such representations remain semantically opaque and unstable under contextual shift. We introduce AURORA, Adaptive Uncertainty aware Representations through Orthogonalized Relational Alignment, a new framework for healthcare representation learning based on contextual latent geometry. Rather than optimizing a single unified embedding manifold, AURORA decomposes representations into orthogonal semantic subspaces corresponding to distinct contextual factors and learns relational consistency objectives within each subspace. This induces latent spaces that are both semantically disentangled and geometrically interpretable. Across multiple clinical prediction and retrieval tasks, AURORA consistently outperforms reconstruction, contrastive, and self distillation baselines while substantially improving contextual disentanglement, neighborhood purity, and robustness under institutional distribution shift. Our results suggest that latent geometry itself constitutes an important axis of healthcare foundation model design and that explicitly structuring representation space according to contextual semantics provides a complementary direction beyond conventional predictive compression objectives.

Yuanyun Zhang, Shi Li

University of the Chinese Academy of Sciences · Columbia University

Disentangled Representation Learning Representation Learning Healthcare Orthogonal Representation Learning Geometric Representation Learning

May 7, 2026cs.LG

The E $Δ$ -MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality

We present the E

Δ

-MHC-Geo Transformer, a novel architecture that unifies Manifold-Constrained Hyper-Connections (mHC), Deep Delta Learning (DDL), and the Cayley transform to obtain input-adaptive, unconditionally orthogonal residual connections. Unlike DDL, whose Householder operator is orthogonal only at

β\in \{0,2\}

, our Data-Dependent Cayley rotation

Q(x)=(I+(β/2)A(x))^{-1}(I-(β/2)A(x))

preserves orthogonality for all

β

and all inputs. To handle negation, an eigenvalue

-1

case that Cayley provably excludes, we introduce the E

Δ

-MHC-Geo Hybrid, which combines Cayley rotation with Householder reflection via a learned operator-selection gate

X'=γ(X)Q(X)X+(1-γ(X))H_2(X)X

. A midpoint-collapse regularizer,

4γ(1-γ)

, encourages boundary gate decisions, where each selected component is orthogonal. In matched-parameter comparisons, with approximately 1.79M parameters per model and mean +/- standard deviation over 3 seeds, against four baselines including the concurrent JPmHC, E

Δ

-MHC-Geo achieves the best long-horizon stability, 1.9x over JPmHC and 3.8x over GPT; the best near-

π

rotation loss, 4.5x over JPmHC on single-plane; strong norm preservation, with 0.001 mean deviation; and 0.96 negation cosine alignment in a diagnostic reflection probe, all with 33% fewer layers. While JPmHC's wider representation excels on pure rotation, its finite Cayley residual mixer excludes an exact

λ=-1

operator and has no reflection branch, motivating our hybrid approach for accessing both connected components of

O(n)

.

Arash Shahmansoori

Independent Researcher

Transformer Residual Learning Hyper-Connections Orthogonal Representation Learning

May 5, 2026cs.LG

Disentangling Shared and Task-Specific Representations from Multi-Modal Clinical Data

Real-world clinical data is inherently multimodal, providing complementary evidence that mirrors the practical necessity of jointly assessing multiple related outcomes. Although multi-task learning can improve efficiency by sharing information across outcomes, existing approaches often fail to balance shared representation learning with outcome-specific modeling. Hard parameter sharing can trigger negative transfer when task gradients conflict, while flexible sharing may still entangle shared and task-specific signals. To address this, we propose a multi-task framework built on a unified Transformer for multimodal fusion, augmented with Orthogonal Task Decomposition (OrthTD) to split patient representations into shared and task-specific subspaces and impose a geometric orthogonality constraint to reduce redundancy and isolate task-specific signals. We evaluated OrthTD on a real-world cohort of 12,430 surgical patients for predicting four outcomes. OrthTD achieved average AUC (area under the receiver operating characteristic curve) of 87.5% and average AUPRC (area under the precision-recall curve) of 37.2%, consistently outperformed advanced tabular and multi-task methods. Notably, OrthTD achieves substantial gains in AUPRC, indicating superior performance in identifying rare events within imbalanced clinical data. These results suggest that enforcing non-redundant shared and task-specific representations can improve multi-outcome prediction from multimodal clinical data.

He Lyu, Huolin Zeng, Junren Wang +7

Department of Anesthesiology and West China Biomedical Big Data Center West China Hospital, Sichuan University, Chengdu, China · Med-X Center for Informatics, Sichuan University, Chengdu, China · Department of National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, Chengdu, China +4

Disentangled Representation Learning Representation Learning Clinical Outcome Prediction Multi-Task Learning Orthogonal Representation Learning Multimodal Fusion

Apr 18, 2026cs.LG

CCAR: Intrinsic Robustness as an Emergent Geometric Property

Standard supervised learning optimizes for predictive accuracy but remains agnostic to the internal geometry of learned features, often yielding representations that are entangled and brittle. We propose Class-Conditional Activation Regularization (CCAR) to explicitly engineer the feature space, imposing a block-diagonal structure via a soft inductive bias. By shaping the latent representation to confine class energy to orthogonal subspaces, we create an intrinsic geometric scaffold that naturally filters noise and adversarial perturbations. We provide theoretical analysis linking this structural constraint to the maximization of the Fisher Discriminant Ratio, establishing a formal connection between geometric disentanglement and algorithmic stability. Empirically, this approach demonstrates that robustness is an emergent property of a well-engineered feature space, significantly outperforming baselines on label noise and input corruption benchmarks.

Akash Samanta, Manish Pratap Singh, Debasis Chaudhuri

Techno India University, Salt Lake, Kolkata, India · DRDO Young Scientist Laboratory - CT, Chennai, India

Disentangled Representation Learning Representation Learning Algorithmic Stability Neural Network Robustness Adversarial Robustness Orthogonal Representation Learning+2

Feb 27, 2026cs.CV

Compositional Generalization Requires Linear, Orthogonal Representations in Vision Embedding Models

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

Arnas Uselis, Andrea Dittadi, Seong Joon Oh

Tübingen AI Center, University of Tübingen · Helmholtz · Technical University of Munich

Neural Representation Geometry Visual Representation Learning Linear Representation Hypothesis Orthogonal Representation Learning Geometric Representation Learning Compositional Representation Learning+1

Feb 6, 2026cs.LG

From Core to Detail: Unsupervised Disentanglement with Entropy-Ordered Flows

The unsupervised discovery of features that are both semantically meaningful and stable across runs remains a central challenge in representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing flow (NF) framework that augments standard maximum likelihood training with an orthogonality regularizer on the decoder Jacobian. The regularizer is rooted in Independent Mechanism Analysis and encourages geometric disentanglement, and a stochastic estimator makes it tractable at image scale (CelebA at

D=2352

and

12288

). Learned features form near-orthogonal curvilinear coordinates and can be ordered by their

\textit{explained (manifold) entropy}

after training, analogous to the ranking by explained variance in PCA, which turns EOFlows into a non-linear generalization of PCA. EOFlows identify an order of magnitude more stable features than existing methods, and these features emerge in distinguishable categories (global, local, and generic) and support tentative semantic interpretations. The local features have strikingly sparse support in pixel space, although our method never enforces this. Retaining only the most important, i.e. highest entropy, features turns the bijective flow into an autoencoder with adjustable bottleneck, rivaling the rate-distortion performance of dedicated autoencoders.

Daniel Galperin, Ullrich Köthe

Heidelberg University

Unsupervised Learning Disentangled Representation Learning Normalizing Flows Orthogonal Representation Learning Flow-Based Generative Modeling

Feb 4, 2026cs.LG

Towards Isolated Interventions via Almost Orthogonal Features in Language Models

A central premise in mechanistic interpretability is that meaningful concepts in language models are represented by linear features in activation space. For such features to support reliable interventions, manipulating one feature should not substantially alter the effects of others. In practice, however, feature entanglement leads to interference such that localized interventions can have unintended downstream effects. Motivated by the \textit{Independent Causal Mechanisms} principle, we propose to constrain internal features to be almost orthogonal. We argue that this promotes modular representations amenable to causal intervention. We formalize this problem by characterizing the gap between an idealized isolated intervention and its realized effect on model outputs in terms of feature interference. We upper-bound the propagation of feature interference in terms of the self-coherence of the feature dictionary, and relate this discrepancy to an explicit orthogonality regularization on the dictionary itself. Empirically, we show that this regularization enables more isolated interventions on mathematical reasoning concepts while preserving model performance. Our code is available under \texttt{https://github.com/mrtzmllr/sae-icm}.

Moritz Miller, Florent Draye, Bernhard Schölkopf

Max Planck Institute for Intelligent Systems, Tübingen, Germany · ETH Zurich, Switzerland · Max Planck ETH Center for Learning Systems +1

Disentangled Representation Learning Representation Learning Orthogonal Representation Learning Mechanistic Interpretability Causal Interventions in Language Models