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4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 27

Sep 30, 2026cs.RO

CF-JEPA: Improving Robustness of JEPA World Models via Controllability Factorization

Controlling an agent with vision requires being able to separate useful information from irrelevant background information. JEPA-style latent world models seem like a natural approach for this, as they do not perform pixel-level reconstruction; however, they are still sensitive to these distractor signals and experience latent collapse. In this work, we introduce Controllability Factorized JEPA (CF-JEPA), a JEPA-style world model which splits the latent space into controllable and uncontrollable subspaces. This factorization allows us to capture all the distractor information into the uncontrollable region, while we use the control-relevant latent information for our task. With this, we show comparable performance across 2D and 3D control tasks under nominal conditions and improved performance under distracted conditions, where CF-JEPA is the only model that does not experience latent collapse. We also validate our model under distracted conditions for a simulated robot task, highlighting the practical application of such a scheme.

Morgan Byrd, Robert Wright, Sehoon Ha

Georgia Institute of Technology, Atlanta, GA, 30308, USA · Georgia Tech Research Institute, Atlanta, GA, 30308, USA

Representation Learning Representation Collapse Latent World Models Vision-Based Robot Control

Sep 30, 2026cs.SD

Collapse, Not Invariance: Diagnosing Auxiliary Objectives in Speech Anti-Spoofing

Speech anti-spoofing countermeasures degrade when the generator, codec or channel changes, and a common remedy is an auxiliary objective that shapes the embedding space; whether it does is invisible to EER, a pure ranking metric. We compare seven such objectives with cross-entropy over 113 runs on five corpora, AASIST3 at three seeds plus four pre-trained detectors, and measure the embedding space of the 24 AASIST3 runs directly. Raw augmentation displacement makes cosine consistency look effective, but the gain is a smaller space, not a more stable one: normalised by the spread, no configuration consistently improves on cross-entropy. Every trained space is dominated by the single decision axis expected for two classes, whose training-set structure does not transfer, and four runs collapse to a near-constant output that displacement rewards and EER reports as poor accuracy. No auxiliary objective keeps an advantage over cross-entropy across architectures, corpora and seeds.

Ksenia Lysikova, Kirill Borodin, Maxim Maslov +1

Lab260, Yerevan, Armenia · BitmanagerAI, Dubai, UAE · MTUCI, Moscow, Russia

Audio Deepfake Detection Representation Collapse Domain Generalization ASVspoof

Sep 30, 2026cs.LG

Stable Transformers for Graph Generation

Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures should provide greater expressive capacity and a broader receptive field, their effectiveness can decline with depth: repeated self-attention progressively contracts node representations, impeding information flow and gradient propagation. We analyse this phenomenon from a dynamical systems perspective, focusing on how the denoiser's spectral dynamics affect graph generation. We show that standard GT denoisers become increasingly dissipative as depth grows, leading to vanishing gradients and representation collapse. To isolate the effect of these dynamics, we construct a permutation-equivariant GT with inherently stable, non-dissipative transport. We also introduce a damping mechanism that continuously interpolates between non-dissipative and increasingly contractive regimes, enabling a direct assessment of how dissipation influences generation. Experiments on synthetic and molecular graph generation benchmarks show that the gap between these regimes widens with depth: non-dissipative dynamics preserve representation diversity and gradient flow, sustaining strong generative performance, whereas greater contraction progressively impairs it. These findings identify the denoiser's dynamical regime as a key design factor for deep graph generative models.

Luca Miglior, Alessio Gravina, Davide Bacciu

Department of Computer Science, University of Pisa, Italy

Representation Collapse Graph Generation Neural Network Training Dynamics Graph Transformer

Sep 28, 2026cs.CV

Generative Residual Factorization

Under a shared-factor model, the conditional law of the next image patch factors into a posterior over the shared scene factor and a residual kernel given that factor. A sufficient statistic of the past replaces the raw past in the posterior and does not replace the kernel. The conditional entropy splits into residual entropy, which no observation of the factor can remove, and a posterior term, which a better representation of the past can remove. Next-embedding prediction is a directional likelihood on a shallow map, so the fiber of that map is unidentified and a constant embedding remains a minimizer. The same split is an equality in a scalar Gaussian model, evaluated in closed form.

Letian Gong, Yuzhou Hong

Zhejiang University of Science and Technology · Zhejiang Sci-Tech University

Representation Collapse Latent Variable Models Predictive Representation Learning

Aug 8, 2026cs.CV

Three Necessary Principles for Self-Supervised Visual Representation Learning

We argue that learning visual representations without labels requires a training signal jointly complete across three non-overlapping objectives: semantic invariance across augmented views, patch-level spatial prediction, and representational non-degeneracy. We formalize these as the observation, prediction, and regularization principles and prove (i) that combining observation and prediction without regularization admits the constant encoder as a global minimizer under negative-free alignment; (ii) that the two objectives are gradient-complementary and structurally non-conflicting at the encoder output; and (iii) that the momentum encoder converges to the same fixed point as the online encoder and provides no collapse guarantee at convergence. Contrastive alignment provides only self-limiting collapse resistance, formalized via an explicit gradient-decay argument. Dropping prediction withholds the spatial training signal by construction; dropping observation forfeits cross-view semantic invariance by construction; at the scale we study, no pair substitutes for the third. Every major self-supervised method is a special case of a single unified energy decomposition. We pair every theoretical claim with a controlled experiment, including a patch-retrieval evaluation for the spatial consequence of prediction.

Nikos Giakoumoglou, Paschalis Giakoumoglou, Tania Stathaki

Imperial College London · CERTH, ITI

Contrastive Learning Representation Collapse Self-Supervised Learning Self-Supervised Visual Representation Learning

Jul 27, 2026cs.IR

SpecFormer: Mitigating Embedding and Attention Collapse via Spectral-Aware Transformer for Recommendation

Transformer architectures have achieved remarkable success across diverse domains; however, directly applying their standard self-attention mechanism to recommendation often yields suboptimal performance, sometimes even trailing behind well-designed simple recommendation models. In this paper, we reveal that this performance bottleneck stems from severe embedding and attention collapse unique to recommendation scenarios. The heterogeneity and long-tail nature of recommendation data lead to a severe spectral collapse dominated by a few principal singular values. We further theoretically demonstrate that this triggers a vicious cycle in recommendation model's forward and backward propagation, which accelerates embedding and attention collapse and limits the model's scaling capability with increased depth. To address these issues, we propose SpecFormer, a novel Spectral-Aware Transformer designed for mitigating embedding and attention collapse in recommendation. Specifically, SpecFormer introduces 1) a Learnable Spectral Softening module to dynamically smooth the singular values distribution of the input token embeddings; 2) a Spectrum-softened Attention mechanism to model feature interaction under a more uniform spectral distribution space; 3) a Spectral Residual Position Encoding via Taylor expansion of singular values, explicitly providing a spectral inductive bias for feature interactions. Extensive experiments on one industrial and two public datasets demonstrate that SpecFormer significantly outperforms state-of-the-art baselines. Notably, SpecFormer has been successfully deployed in a real-world commercial recommender system and exhibits exceptional scaling capabilities: stacking SpecFormer layers actively improves the attention effective rank and recommendation performance.

Yu Cui, Yi Xu, Jiahao Wang +6

Zhejiang University Hangzhou, China · Alibaba Group Beijing, China

Representation Collapse Transformer Recommender Systems Attention Mechanisms

Jul 26, 2026cs.CL

The JEPA Paradox in Language: The Geometry of Linguistic Alternatives

Joint-Embedding Predictive Architectures (JEPAs) are effective for images, video, and audio, yet deterministic JEPA-style latent prediction has not become a standard objective for text encoders. We argue that this gap reflects a mismatch between squared-error latent prediction and the conditional structure of language. The key requirement is conditional concentration: given a context and target location, the target representation should lie near a single meaningful point. Local image prediction often satisfies this through spatial continuity, whereas masked text can admit multiple valid token or span completions whose representations need not share a coherent center. We formalize this mismatch through three conditions---predictability, non-collapse, and low conditional variance---and show how their failure creates centroid degeneracy and collapse pressure in text. Matched I-JEPA and T-JEPA experiments reveal the predicted sequence: mutual-information saturation and elevated target variance precede train--validation instability, effective-rank degeneration, cosine collapse, and poor downstream transfer. The same pattern appears across five independent data seeds, indicating that it is not a sampling artifact. These results do not rule out predictive learning for language; they show that text-compatible JEPA objectives must preserve multiple plausible completions rather than compress them into a single latent point.

Anh Trac Duc Dinh, Khang Nhat Hoang Vo

Center for AI Research (CAIR), VinUniversity, Hanoi, Vietnam · Faculty of Computer Science and Engineering Ho Chi Minh City University of Technology (HCMUT), VNU-HCM Ho Chi Minh City, Vietnam · Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi, United Arab Emirates

Representation Collapse Masked Language Modeling Joint-Embedding Predictive Architecture Predictive Representation Learning Representation Geometry in Language Models

Jul 16, 2026cs.LG

Depth-Dependent Hidden-State Collapse in Dynamical System Autoencoders for LiDAR Point-Cloud Classification

We study Dynamical System Autoencoders (DSAE) for LiDAR point-cloud classification using spatial coordinates and Product Coefficient feature augmentations. The experiments compare separately trained DSAE architectures at encoder depths

K=1,\ldots,5

and evaluate the resulting hidden representations with Random Forest, kNN, and a majority-class Dummy baseline. The main finding is a hidden-state collapse at

K=5

. For both xyz and xyz plus Product Coefficient inputs, the hidden-state standard deviation falls to the order of

10^{-5}

, while all three classifiers attain the same macro F1 score of

0.224688

. We prove that between-class hidden scatter is bounded by total hidden scatter, which in turn is controlled by the reported hidden-state variance. Thus a nearly constant hidden representation cannot retain substantial class-separating structure. Product Coefficients neither improve pre-collapse macro F1 nor prevent the

K=5

collapse in the present DSAE setting. These results identify large-depth representation collapse as a concrete failure mode for DSAE LiDAR classification.

Patricia Medina, Hy P. G. Lam

Department of Mathematics New York City College of Technology, CUNY Brooklyn, NY, USA · The Graduate Center, CUNY New York, NY, USA · Department of Mathematical Sciences Worcester Polytechnic Institute Worcester, MA, USA

Representation Collapse Latent Dynamics Modeling Point Cloud Classification Autoencoders

Jul 13, 2026cs.LG

How to Tame Grokking: Representation Geometry as a Control Signal

Grokking is a phenomenon in which neural networks initially memorize training data and only later exhibit strong generalization after prolonged optimization. Despite extensive recent study, the factors influencing the emergence and timing of grokking remain incompletely understood. We investigate the relationship between representation geometry and delayed generalization. We find that dimensionality collapse consistently precedes the onset of grokking in all evaluated settings. Motivated by these observations, we introduce Geometric Dimensionality Regularization (GeomDR), a simple spectral regularizer that modifies the effective dimensionality of hidden representations during training. Across modular addition, modular division, and permutation composition tasks, GeomDR consistently alters grokking dynamics and can substantially accelerate the onset of generalization depending on the intervention schedule and target dimensionality. In several settings, grokking is accelerated by up to 52 times relative to standard AdamW training. Similar qualitative effects are observed in both multilayer perceptrons and transformers. Together, these results suggest that representation geometry can serve as an effective control signal for grokking and provide evidence that geometric interventions offer a practical approach for studying and influencing delayed generalization in neural networks.

Maksim A Kazanskii

Independent Researcher

Neural Network Generalization Spectral Regularization Representation Collapse Neural Representation Geometry Neural Network Training Dynamics Grokking

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

Jun 21, 2026cs.LG

All Routes Lead to Collapse

Attention sinks, representation collapse, and norm stratification are treated as transformer-specific pathologies. We show they are not specific to attention: they are what content-based routing does under a fixed similarity metric. We give a reframing identity: softmax attention is Boltzmann-weighted aggregation over Euclidean distances with constant key norms, so its score omits a

-\|k\|^2

term and is blind to key magnitude. This predicts that any router whose metric is ill-matched to its representations should compensate, by concentrating its routing and collapsing the routed representations. We test it on routers that score and aggregate over different axes: softmax attention over tokens (nine pretrained transformers), graph attention over nodes, a selective state-space model and a recurrent mixer over time, and learned residuals over depth. All develop the same signature, and two within-model ablations show it is caused by the routing mechanism rather than by incidental dynamics. The form is contingent, set by the strength of the positional brake each router carries alongside its content score; we sweep that brake and move the onset across its whole range. The mechanism is not contingent, and it does not require norm stratification: a router with norm-normalized keys concentrates just the same. We do not claim these models implement Riemannian geometry; the geometric view is a diagnostic that names the inadequacy of the flat, norm-blind metric.

K. R. Balasubramanian

Independent Research

Representation Collapse Attention Sinks Attention Mechanisms

Jun 2, 2026cs.CV

Template Collapse and Information-Theoretic Limits in Camera rPPG Pulse Morphology Restoration

Objective: Consumer face camera remote photoplethysmography (rPPG) enables passive cardiovascular monitoring, but whether single-cycle waveform morphology encoding arterial stiffness biomarkers is recoverable from this measurement has not been characterised. Methods: We evaluated 16 architectures spanning six families on 153 subjects across three datasets, introducing cross-subject Pearson r to distinguish subject-specific recovery from template collapse. Results: No architecture recovered subject-specific morphology (cross-subject r range 0.773--0.9999; ground-truth ceiling 0.601). Supervised Contrastive (SupCon) converged to log N = 4.844, constituting the strongest available empirical evidence that no discriminative morphological structure is extractable from single-cycle rPPG by the encoder families tested. The VAE decoder restores population-level harmonic content absent from the rPPG input (H2/H1: 0.310 output vs. 0.275 input), generalising zero-shot to UBFC (r = +0.708); a directional hallucination gap (p = 0.150) suggests partial signal reading. Anti-collapse objectives fail when input carries no discriminative structure. Significance: Consumer cameras cannot encode individual arterial morphology; cross-subject r is a necessary collapse diagnostic for waveform reconstruction benchmarks.

Achraf Ben Ahmed

PlesmoSense SARL

Remote Photoplethysmography Representation Collapse Photoplethysmography

Jun 1, 2026cs.CV

VISReg: Variance-Invariance-Sketching Regularization for JEPA training

Self-supervised learning methods prevent embedding collapse via modeling heuristics or explicit regularization of the embedding space. Among the latter, VICReg decomposes regularization into variance and covariance objectives, offering flexibility and interpretability. However, covariance captures only second-order statistics -- encouraging decorrelation but failing to enforce the full distributional shape needed for stable training. Sketching-based methods such as SIGReg address this by aligning embeddings to an isotropic Gaussian, but lack flexibility and suffer from vanishing gradients under collapse. We propose Variance-Invariance-Sketching Regularization (VISReg), which replaces covariance with a Sliced-Wasserstein-based sketching objective that enforces full distributional shape, while retaining a variance term for scale control. By decoupling scale and shape, VISReg combines VICReg's flexibility with the distributional rigor of sketching methods, providing robust gradients even under collapse. We show that VISReg scales linearly, outperforms existing regularization on low-quality datasets, and is resilient to long-tailed and low-rank regimes. Pre-trained on ImageNet-1K, VISReg achieves state-of-the-art performance on out-of-distribution datasets. Pre-trained on ImageNet-22K, it matches DINOv2's OOD performance despite the latter using 10x more data (LVD-142M). Project and code: https://haiyuwu.github.io/visreg.

Haiyu Wu, Randall Balestriero, Morgan Levine

Altos Labs · Brown University

Representation Collapse Joint-Embedding Predictive Architecture Sliced Wasserstein Distance Self-Supervised Visual Representation Learning

May 28, 2026cs.LG

Representation Collapse in Sequential Post-Training of Large Language Models

Large language models are now adapted through chains of post-training stages rather than through a single instruction-tuning pass. This paper studies whether such sequential post-training gradually compresses internal representations into low-rank, anisotropic, and homogeneous feature spaces. We define a measurement suite for hidden states, logits, token trajectories, and LoRA updates, and we use it to analyze supervised fine-tuning, preference optimization, safety/refusal tuning, math and code specialization, and long chain-of-thought tuning under controlled stage orderings. The central hypothesis is that excessive representation concentration is not merely a geometric curiosity: it predicts reduced plasticity during later adaptation, weaker out-of-domain generalization, and poorer calibration. We further evaluate lightweight interventions, including mixed-domain replay, feature refresh, representation diversity regularization, and LoRA update decorrelation, as ways to preserve future learnability without giving up the behavioral gains of post-training.

Yichen Liu, Mingyu Chen, Hao Wang +7

Hangzhou Dianzi University · Zhejiang Gongshang University · Ningbo University +1

Continual Learning for LLMs Representation Collapse LLM Post-Training Representation Geometry in Language Models

May 22, 2026cs.LG

Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation

Scaling recommendation models is a central challenge in recommender systems. Recently, RankMixer has emerged as an effective solution, operating on a unified token representation and alternating between token mixing and per-token feedforward networks (P-FFNs) to achieve scalable performance. However, RankMixer suffers from \textit{embedding collapse}, where learned representations have low effective rank, limiting expressivity and underutilizing the expanded representation space. Through empirical analysis and theoretical insights, we identify rigid token mixing and P-FFN modules as the primary causes of this phenomenon, jointly inducing a \textbf{damped oscillatory trajectory} in effective-rank evolution across layers. To address it, we propose RankElastor, a novel architecture that produces spectrum-robust representations with provable collapse mitigation. RankElastor introduces two components: (i) \textbf{parameterized full mixing}, which enables expressive token mixing with improved spectral robustness; and (ii) \textbf{GLU-improved P-FFNs}, which stabilize representation spectra through GLU-style FFN modules. Extensive experiments on large-scale industrial datasets demonstrate that RankElastor consistently improves recommendation performance, mitigates embedding collapse, and exhibits robust scaling behavior. Code is available at this GitHub repository: https://github.com/vasile-paskardlgm/RankElastor

Guoming Li, Shangyu Zhang, Junwei Pan +7

The Hong Kong University of Science and Technology (Guangzhou) Guangzhou, China · Tencent Inc. Shenzhen, China

Representation Collapse Recommender Systems

May 12, 2026cs.HC

How Well Do Large Language Models Capture Human Personality?

Large language models (LLMs) are increasingly used to simulate human populations via persona prompting, often under the assumptions that richer persona descriptions improve behavioral fidelity, similarly sized attribute combinations are equally simulatable, and persona definitions generalize across tasks. In this work, we formalize these assumptions and systematically evaluate them across multiple architectures, scales, and simulation settings. We identify a fundamental limitation we term persona manifold collapse, where increasingly expressive persona specifications lead to systematic contraction of representational and behavioral diversity. Across models, increasing persona complexity consistently reduces inter-persona separation in latent space and weakens behavioral differentiation in downstream simulation tasks. These effects persist across multiple analyses as richer personas fail to preserve human subgroup disagreement, performance varies across attribute combinations of similar size, and adding descriptive detail often degrades rather than improves simulation fidelity. Surprisingly, simple Age-Gender personas consistently outperform richly specified Ideal Customer Profiles (ICPs) across industries, achieving substantially higher downstream prediction accuracy. We find that collapse is not uniform across attributes. Certain combinations remain behaviorally stable and preserve stronger alignment with human responses, forming localized regions we term alignment bridges. Together, our results provide empirical and conceptual foundations for understanding the limits of persona-conditioned simulation, highlighting the need for representation-aware persona construction rather than increasing persona expressivity alone.

Aanisha Bhattacharyya, Yaman Kumar Singla, Rajiv Ratn Shah +2

Adobe Media and Data Science Research (MDSR) · IIIT-Delhi · SUNY at Buffalo

LLM Evaluation Representation Collapse Large Language Model-Based Role-Play Simulation Personality Modeling in Language Models Human Behavior Simulation Large Language Model-Based Social Simulation+1

May 11, 2026cs.LG

Optimal Representations for Generalized Contrastive Learning with Imbalanced Datasets

In this paper, we provide a computable characterization of the geometry of optimal representations in Contrastive Learning (CL) when the classes are imbalanced. When classes are balanced and the representation dimension is greater than the number of classes, it is well-known that the optimal representations exhibit Neural Collapse (NC), i.e., representations from the same class collapse to their class means and the class means form an Equiangular Tight Frame (ETF). For imbalanced classes and a large, generalized family of CL losses, we prove that the optimal representations of all samples from the same class collapse to their class means and their geometry exhibits an angular symmetry structure that is determined by the relative class proportions. In general, we show that the geometry can be determined by solving a convex optimization problem. Exploiting this symmetry structure, we analytically investigate a special case where class imbalance is extreme and prove that CL exhibits a phenomenon called Minority Collapse (MC) where all samples from the minority classes (classes with small probabilities) collapse into a single vector, whenever the class imbalance exceeds a threshold, which in turn depends on the regularity properties of the CL loss used and on the number of negative samples. Numerical results are provided to illustrate these phenomena and corroborate the theoretical results. We conclude by identifying a number of open problems.

Thuan Nguyen, Shuchin Aeron, D. Richard Brown +1

Department of Engineering, Engineering Technology East Tennessee State University · Department of Electrical and Computer Engineering Tufts University · Department of Electrical and Computer Engineering Worcester Polytechnic Institute +1

Class-Imbalanced Learning Contrastive Learning Representation Collapse Neural Representation Geometry Neural Collapse

May 10, 2026cs.LG

Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models

Joint-Embedding Predictive Architectures (JEPAs) provide a simpleframework for learning world models by predicting future latent representations.However, JEPA training is subject to a bias-variance tradeoff.Without sufficient structural constraints, excessive representationalvariance causes the model to collapse to trivial solutions.The recent LeWorldModel (LeWM) shows that this issue can be alleviated bysimply constraining latent embeddings with an isotropic Gaussian prior.However, latent representations inherently lie on low-dimensional manifoldswithin a high-dimensional ambient space, and enforcing an isotropic Gaussianprior directly in this ambient space introduces an overly strong bias.In this work, we propose ame, which seeks a favorable operatingpoint on the bias-variance frontier by applying Gaussian constraints inmultiple random subspaces rather than in the originalembedding space.This design relaxes the global constraint while preserving itsanti-collapse effect, leading to a better balance between trainingstability and representation flexibility.Extensive experiments across fourcontinuous-control environments demonstrate that consistentlyoutperforms LeWM with very clear margins.Our method is simple yet effective, and serves as a strong baseline for future JEPA-based world model research.fdefinedeeemodeThe code is available at https://github.com/intcomp/Sub-JEPA.

Kai Zhao, Dongliang Nie, Yuchen Lin +4

1Shanghai University · 2The University of Manchester · 3Nankai University

Representation Learning Representation Collapse World Model Learning Joint-Embedding Predictive Architecture

May 8, 2026cs.LG

Enhancing Federated Quadruplet Learning: Stochastic Client Selection and Embedding Stability Analysis

Federated Learning (FL) enables decentralised model training across distributed clients without requiring data centralisation. However, the generalisation performance of the global model is usually degraded by data heterogeneity across clients, particularly under limited data availability and class imbalance. To address this challenge, we propose FedQuad, a novel method that explicitly enforces minimising intra-class representations while enabling inter-class splits across clients. By jointly minimising distances between positive pairs and maximising distances between negative pairs, the proposed approach mitigates representation misalignment introduced during model aggregation. We evaluate our method on CIFAR-10, CIFAR-100, and Tiny-ImageNet under diverse non-IID settings and varying numbers of clients, demonstrating consistent improvements over existing baselines. Additionally, we provide a comprehensive analysis of metric learning-based approaches in both centralised and federated environments, highlighting their effectiveness in alleviating representation collapse under heterogeneous data distributions.

Ozgu Goksu, Nicolas Pugeault

School of Computing Science University of Glasgow

Representation Collapse Non-IID Federated Learning Metric Learning Federated Learning

May 7, 2026cs.LG

Mean Mode Screaming: Mean--Variance Split Residuals for 1000-Layer Diffusion Transformers

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

Pengqi Lu

Beijing, China

Deep Learning Optimization Representation Collapse Diffusion Transformer Residual Learning

Apr 30, 2026cs.CL

Lost in State Space: Probing Frozen Mamba Representations

Mamba's recurrent state h_t is, by construction, a compressed summary of every token seen so far. This raises a tempting hypothesis: if we extract token-level outputs y_t at fixed patch boundaries, we obtain semantic sentence summaries for free, with no pooling head, no fine-tuning, and no [CLS] token. We test this hypothesis carefully. Across five benchmarks (SST-2, CoLA, MRPC, STS-B, IMDb), we compare four strategies for extracting frozen sentence representations from a pretrained Mamba-130M backbone under a strict frozen-feature probing protocol, using three random seeds where computationally feasible. The results do not support the hypothesis: patch boundary readouts do not consistently outperform simple mean pooling. We identify and quantify two structural pathologies: severe anisotropy (mean pairwise cosine similarity 0.9999, std 0.000044) and representational collapse in the raw final SSM state (MCC = 0.000 on CoLA across all three seeds, confirmed via confusion matrix). We further propose orthogonal injection, a modified recurrence that constrains new information per

Bhagyashree Wagh, Akash Singh

University of Washington · University of Florida

Representation Geometry Representation Collapse Sentence Embeddings State Representation Learning State Space Models

Apr 30, 2026cs.IT

Why Self-Supervised Encoders Want to Be Normal

Self-supervised learning has achieved remarkable empirical success in learning robust representations without explicit labels, most recently demonstrated within the framework of Joint-Embedding Predictive Architectures (JEPA). However, a fundamental question remains: what analytical principles drive these encoders toward specific distributional states? In this paper, we demonstrate that the preference for normal distributions in self-supervised encoders is a direct consequence of the Information Bottleneck (IB) principle. By recasting the IB objective as a rate-distortion problem over the predictive manifold, we provide a theoretical basis for why optimal, target-neutral, latent representations should tend towards isotropic Gaussian states. Under this framework, we show that latent representations correspond to soft clustering of inputs sharing similar predictive distributions, organized within a natural simplex structure. This perspective unifies a wide range of existing supervised and less-supervised objectives and provides a principled explanation for commonly used regularization schemes. Furthermore, we derive practical loss objectives that approximate this structure and demonstrate their effectiveness on standard benchmarks. Ultimately, our framework offers a geometric lens to understanding representation collapse and it establishes a mathematical system for regularization strategies to be used to ensure high-entropy, informative embeddings in modern self-supervised models.

Yuval Domb

Representation Collapse Self-Supervised Learning Rate-Distortion Theory Joint-Embedding Predictive Architecture Information Bottleneck Predictive Representation Learning

Apr 28, 2026cs.LG

Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index

Representational collapse, where embeddings become anisotropic and lose multi-scale structure, can erode downstream performance long before performance metrics react. We propose an online, topology-aware monitor for evolving neural representations that couples Modular Morse Homology Maintenance (MMHM) with a composite Collapse Index (CI). Instead of rebuilding complexes each epoch, we apply sparse edits at a fixed scale and maintain a discrete Morse matching, yielding fast, incremental updates. Across LLM fine-tuning and temporal KGE training, CI provides a low-latency early-warning signal suitable for in-training interventions. Code and experimental scripts will be released publicly

Alexander Kalinowski

SUNY Empire

Representation Collapse Neural Representation Geometry Neural Network Training Dynamics Topological Data Analysis

Apr 27, 2026cs.LG

Complexity of Linear Regions in Self-supervised Deep ReLU Networks

There has been growing interest in studying the complexity of Rectified Linear Unit (ReLU) based activation networks. Recent work investigates the evolution of the number of piecewise-linear partitions (linear regions) that are formed during training. However, current research is limited to examining the complexity of models trained in a supervised way. Self-Supervised Learning (SSL) differs in that it directly optimises the representation space using a loss function to enhance the model's performance across multiple downstream tasks. This study investigates the local distribution of linear regions produced by SSL models. We demonstrate that the evolution of linear regions correlates with the representation quality by utilising SplineCam to extract two-dimensional polytopes near the data distribution. We track the number, area, eccentricity, and boundaries of regions throughout training. The study compares supervised, contrastive, and self-distillation methods over two standard benchmark datasets, MNIST and FashionMNIST. The analysis of the experimental results shows that self-supervised methods create substantially fewer regions to achieve comparable accuracy to supervised models. Contrastive methods rapidly expand regions over time, whereas self-distillation methods tend to consolidate by merging neighbouring regions. Lastly, we can detect representation collapse early within the geometric space of linear regions. Our analysis suggests that polytopal metrics can serve as reliable indicators of representation quality and model performance.

Mufhumudzi Muthivhi, Terence L. van Zyl

University of Johannesburg, Johannesburg, South Africa

Representation Collapse Self-Supervised Visual Representation Learning

Apr 26, 2026cs.LG

Rank, Head-Channel Non-Identifiability, and Symmetry Breaking: A Precise Analysis of Representational Collapse in Transformers

A widely cited result by Dong et al. (2021) showed that Transformers built from self-attention alone, without skip connections or feed-forward layers, suffer from rapid rank collapse: all token representations converge to a single direction. The proposed remedy was the MLP. We show that this picture, while correct in the regime studied by Dong, is incomplete in ways that matter for architectural understanding. Three results are established. First, layer normalisation is precisely affine-rank-neutral: it preserves the affine rank of the token representation set exactly. The widespread claim that LN "plays no role" is imprecise; the correct statement is sharper. Second, residual connections generically obstruct rank collapse in real Transformers such as BERT-base, in a measure-theoretic sense, without contribution from the MLP. The MLP's irreplaceable function is different: generating feature directions outside the linear span of the original token embeddings, which no stack of attention layers can produce. Third, a phenomenon distinct from rank collapse is identified: head-channel non-identifiability. After multi-head attention sums per-head outputs through the output projection, individual contributions cannot be canonically attributed to a specific head; n(H-1)d_k degrees of freedom per layer remain ambiguous when recovering a single head from the mixed signal. The MLP cannot remedy this because it acts on the post-summation signal. A constructive partial remedy is proposed: a position-gated output projection (PG-OP) at parameter overhead below 1.6% of the standard output projection. The four collapse phenomena identified in the literature -- rank collapse in depth, in width, head-channel non-identifiability, and entropy collapse -- are unified under a symmetry-breaking framework, each corresponding to a distinct symmetry of the Transformer's forward pass.

Giansalvo Cirrincione

aLaboratoire LTI, Université de Picardie Jules Verne, Chemin du Thil, 80025 Amiens, France

Transformer Interpretability Representation Collapse Parameter Identifiability Self-Attention Symmetry Breaking Transformer Attention+2

Jan 29, 2026cs.CV

Hypersolid: Emergent Vision Representations via Short-Range Repulsion

A central problem in self-supervised learning is preventing representation collapse. Most methods avoid it through global mechanisms, such as contrastive expansion, variance constraints, decorrelating dimensions, or enforcing certain output distributions. In this work, we study a different design: short-range repulsion. We introduce Hypersolid, a self-supervised objective that combines view alignment with local collision avoidance. Our method induces a latent geometry of compact, semantically aligned neighborhoods with low anisotropy. This geometry is especially effective for unsupervised clustering and fine-grained separation, although it comes at the cost of weaker transferability.

Esteban Rodríguez-Betancourt, Edgar Casasola-Murillo

Posgrado en Computación e Informática, Universidad de Costa Rica, San José, Costa Rica · Escuela de Ciencias de la Computación e Informática, Universidad de Costa Rica, San José, Costa Rica

Unsupervised Learning Representation Learning Representation Collapse Self-Supervised Visual Representation Learning

Feb 13, 2025cs.LG

You Do Not Fully Utilize Transformer's Representation Capacity

In contrast to RNNs, which compress their history into a single hidden state, Transformers can attend to all past tokens directly. However, standard Transformers rely solely on the hidden state from the previous layer to represent the entire context. We show that this design creates pressure toward representation collapse and can degrade performance. To address this issue, we introduce Layer-Integrated Memory (LIMe), a lightweight extension that leverages existing key-value buffers and learns per-head, per-layer routing weights to integrate representations from previous layers. Across language modeling, synthetic reasoning, and deep architectures, LIMe improves perplexity per FLOP in the studied regimes and yields strong gains on synthetic tasks while preserving higher value-vector entropy and token separability. Finally, learned routing weights reveal systematic reuse of local and long-distance features, showing how LIMe enriches attention-time memory without increasing hidden-state size. Code is available at https://github.com/corl-team/lime.

Gleb Gerasimov, Yaroslav Aksenov, Nikita Balagansky +2

1T-Tech · 2Moscow Institute of Physics and Technology · 3HSE University

Representation Collapse Memory-Augmented Language Models Self-Attention Transformer Attention Attention Mechanisms