Representation Quality

Learning world models from offline trajectories enables agents to accomplish different tasks through planning. Object-centric (OC) representations, which decompose a scene into a set of slots that bind to its objects, have been proposed as an inductive bias for world models that are more sample-efficient and generalize better. Yet prior object-centric world models (OCWMs) take the slot encoder as given and evaluate only in-distribution, leaving open whether the object-centric bias actually delivers for planning and what within the OCWM drives it. We conduct a controlled study of OCWMs for visual model-predictive control along two axes: object-centric representation quality and generalization under distribution shift relative to scene-centric models. We find that (i) planning success correlates positively with unsupervised slot-quality metrics (FG-ARI, mBO), though the gains saturate at high slot quality; (ii) with well-bound slots, the auxiliary proprioception inputs and masking inductive bias that prior methods relied on become unnecessary; and (iii) under unseen distribution shifts, the OCWM with well-bound slots is more robust overall than the end-to-end trained scene-centric LeWM, while DINO-WM, built on similar frozen pretrained features, remains competitive -- pointing to pretrained features as a key contributor to robustness.

In this work, we study the information bottleneck under perfect privacy, with particular emphasis on the active-rate regime, where the representation-rate constraint is binding and directly limits the achievable utility. The goal is to construct a representation that preserves utility-relevant information while remaining statistically independent of a sensitive variable. This exact independence requirement introduces an additional constraint beyond the classical rate-relevance tradeoff and must be explicitly incorporated into the optimization. To this end, we develop an alternating direction method of multipliers (ADMM)-based method tailored to the resulting problem structure. Under suitable regularity conditions, we establish global convergence of the generated sequence, characterize its convergence rate through the Kurdyka-Lojasiewicz exponent, and extend the analysis to inexact block updates.

Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities. Despite this progress, how such representations behave under continual learning poses fundamentally different challenges that remain underexplored. This work provides a geometric perspective on this problem and establishes a theoretical foundation for representation preservation in hyperbolic space, showing that preventing forgetting requires cross-modal invariance under a shared hyperbolic isometry. We further show that forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion, motivating preservation of both cross-modal relational structure and hierarchical geometry. Guided by these insights, a principled continual learning framework is derived that preserves essential geometric structure while allowing effective adaptation to new tasks. Experiments on continual multimodal benchmarks corroborate the effectiveness of the proposed approach.

Autonomous agents now carry out entire data analyses, selecting cohorts, joining tables, and fitting models with little step-by-step supervision. When such an analysis turns out to be wrong, someone must determine which operation caused it. A recent approach does this without any labelled mistakes, learning instead from analyses known to be sound and flagging operations that depart from what that model predicts; how reliable such audits are has not been studied. This paper supplies that analysis. The choice of score determines whether an error can be localized at all. If each operation is scored by how surprising it is given the operation immediately preceding it, then operations that merely inherit an earlier error are indistinguishable from correct ones, so one mistake produces one flag; scores computed against a longer reconstruction of the intended analysis instead spread a single mistake across many operations. We quantify how far they spread, and how to choose the comparison length when an error accumulates gradually rather than at once. We then give procedures that control the proportion of falsely flagged operations within a single audited analysis, requiring only that sound analyses be exchangeable rather than that the fitted model be correct, and we quantify how much the guarantees weaken when the model is imperfect or when the analysis was selected for review in a way that depends on its content. Finally we establish a limit on what any such audit can report: errors below a certain magnitude cannot be attributed at all, being indistinguishable from ordinary variation among sound analyses. This limit falls so slowly as more sound analyses are collected that at the representation sizes now in use a hundredfold increase reduces it by under two percent, so the dimension of the representation rather than the volume of training data is the binding constraint.

Recent advances in Diffusion Transformers (DiTs) have enabled remarkable progress in visual synthesis, benefiting from their superior scalability. To facilitate DiTs' capability of capturing meaningful internal representations, recent works such as REPA incorporate external pretrained encoders for representation alignment. However, the underlying mechanisms governing representation learning within DiTs remain poorly understood in the community. To this end, this paper first presents a systematic analysis of the representation dynamics of DiTs via quantifying the diversity of block-wise representations. Specifically, we introduce a novel metric, termed the Weighted Diversity Score (WDS), to measure the representational discrepancies across different blocks. Through extensive investigations on the evolution and influence of internal representations under various settings, we reveal that representation diversity across blocks is a critical factor for effective representation learning in DiTs. More importantly, WDS exhibits a strong correlation with synthesis quality across diverse settings, model scales, and training stages (Pearson's $r=-0.869$ with $\log(\text{FID})$), suggesting its potential as an indicator to reflect model performance and a principled guide for model optimization. Based on this key finding, we propose DiverseDiT++, a novel framework that explicitly promotes diverse representation learning. Concretely, our method incorporates long residual connections to diversify input representations across blocks and a representation diversity loss to encourage blocks to learn distinct features. Extensive experiments on ImageNet $256\times256$ and $512\times512$ demonstrate that our DiverseDiT++ yields consistent performance gains and convergence acceleration when applied to different backbones with various sizes,...

Next-destination prediction in continuous-time dynamic graphs (CTDGs) commonly ranks an observed interaction against sampled negative destinations. The resulting score is conditional on both the negative distribution and the number of candidates chosen by the researcher. We show that a non-uniform negative distribution changes the Bayes-optimal ranking, while even a finite candidate set drawn uniformly can destabilize model rankings and measured module effects. Time-varying source-destination history membership and model operations that use this information directly transmit the sampler's influence to the evaluation score. We examine this mechanism using a factorial evaluation of repeated and new positives against seen and unseen negatives, a minimal scorer based solely on pair-history membership, and controlled representation interventions. Across six models on LastFM, MOOC, Reddit, and Wikipedia, at least one model pair changes relative order between the expected Uniform-20 metric and the full catalog on three of the four datasets. The measured effect of the same module also changes in magnitude and direction with the candidate-set size and training objective. These results establish that model-superiority and ablation conclusions from sampled-negative benchmarks are conditional on the stated candidate configuration. All-entity ranking evaluates every destination in a fixed catalog, eliminating negative-selection freedom and sampling variation while retaining the original CTDG scorer. We therefore recommend all-entity ranking as the primary evidence for architecture comparisons on CTDG benchmarks with an enumerable, fixed destination catalog.

Understanding and exploiting the training dynamics of overparameterized deep neural networks remains a central challenge in modern machine learning. Recent evidence on Neural Collapse (NC) shows that class representations and classifiers exhibit highly structured geometry, while the Tunnel Effect suggests that only a subset of layers is essential for feature extraction. We combine these two perspectives and propose an NC-inspired training framework for simplifying deep networks during training. Our method monitors representation dynamics through the Inverse Fisher Criterion, a stable and efficient proxy for the variability collapse behavior, to identify both the split point between feature extraction and classification and the training stage at which simplification becomes viable. We then replace the trailing layers with a lightweight classification head and continue training the reduced model. Experiments on image-classification benchmarks across MLP, VGG, and ResNet architectures show that the proposed method achieves substantial parameter reductions while maintaining accuracy comparable to that of the full model. Code to reproduce the experiments can be found at: https://github.com/LorenzoSciandra/NNS.

Pretrained molecular encoders are commonly evaluated through downstream prediction, but predictive accuracy alone does not establish that a learned representation captures reproducible scientific structure, adds information beyond strong conventional baselines, or transfers out of distribution. We present a reliability-aware audit of generic molecular representations for human olfaction across four distinct claims: global perceptual geometry, incremental predictive value beyond chemistry, cross-dataset replication, and mixture transfer to unseen components. Using the Keller-Vosshall and Bierling single-molecule rating datasets and the Ma binary-mixture dataset, we compare MoLFormer and ChemBERTa against RDKit descriptors and Morgan fingerprints under identity-controlled and matched evaluations. Human three-attribute rating geometry, based on intensity, pleasantness, and familiarity, is reproducible across participant splits (median RSA 0.743 and 0.855), whereas model-human alignment is substantially weaker (RSA 0.019-0.158). Learned embeddings do not consistently outperform conventional representations in global alignment, and MoLFormer provides no clear incremental predictive value beyond a combined RDKit-Morgan baseline in either single-molecule dataset. Human geometry shows positive but incomplete agreement across 63 shared molecules (RSA 0.331; 95% bootstrap interval [0.204, 0.507]). Under one strict unseen-component mixture split, incremental effects are outcome- and representation-dependent, with all intervals crossing zero. These results establish empirical boundaries for the evaluated generic molecular encoders and motivate a broader evaluation principle: representation quality in scientific domains should be assessed separately for target reliability, structural alignment, incremental information, replication, and out-of-distribution transfer.

Large language models (LLMs) have been applied to sequential recommendation by formulating it as a natural language task. Previous work has improved personalization by incorporating collaborative and sequential signals through input conditioning or LLM fine-tuning. However, existing approaches often rely on one or more of the following: LLM fine-tuning, additional architectural modules, representation distillation, or item-level conditioning over long interaction histories, increasing training complexity and deployment cost. We propose REPREC, a lightweight framework that reformulates LLM-based sequential recommendation through lightweight user representation alignment. REPREC maps a fixed-size user embedding from a frozen sequential encoder into a small set of learned soft tokens through a lightweight MLP injector that conditions a frozen LLM, leaving both pretrained backbones unchanged while training only the injector. We conducted exhaustive experiments on multiple benchmark datasets and demonstrate that REPREC consistently outperforms LoRA while remaining compatible with different pretrained sequential encoders and LLM backbones, enabling a modular and production-friendly recommendation pipeline without modifying either pretrained component. The gains are particularly pronounced for casual and core users across all datasets, highlighting REPREC's effectiveness in low-data regimes. Finally, when trained on short prompt histories and evaluated with longer contexts, REPREC maintains 85-100% of LoRA's performance while reducing per-epoch training time by an average of 1.51X, demonstrating an effective balance between recommendation quality and computational efficiency for production deployment. The code is available at https://github.com/phdbotcode/REPREC

Multimodal Contrastive Learning (CL) has shown significant performance in aligning representations across various data modalities and improving downstream tasks, especially in healthcare. It works by minimizing the distance between matched (positive) data modalities, while maximizing the distance between mismatched (negative) samples. Traditional CL frameworks typically assume instance-based correspondence within data batches, treating all non-paired samples as negatives. However, this assumption often fails in medical settings, where samples may share high-level semantic attributes, leading to false negatives that degrade representation quality. In this paper, we propose Multimodal Semantic-Aware Contrastive Learning (MseaCL), a CL framework trained on a pediatric cohort of 3D brain magnetic resonance imaging (MRI) scans and radiology reports. The goal of this framework is to mitigate the impact of semantically similar false negative samples by incorporating semantic similarity between radiology reports, as a guiding signal during the learning process. Our results indicate that applying this framework as a pretraining stage can achieve notable improvements in downstream tasks, e.g., at least a 22.6% increase in the area under the receiver operating characteristic curve (AUC) of pediatric brain tumor molecular classification, demonstrating its potential for more robust and semantically aligned multimodal representations in clinical applications.

We propose NetinfoGC, a framework for graph classification that extends the Network Usable Information (NUI) paradigm to graph-level learning. Unlike conventional graph neural network approaches that rely on end-to-end training of black-box embeddings, NetinfoGC constructs a family of permutation-invariant graph representations derived from propagation-based mechanisms and classical structural descriptors, including graph centrality measures. To evaluate representation quality, we introduce a training-free NUI estimation procedure based on clustering consistency with ground-truth labels, providing a proxy for task-relevant information without supervised learning. We further exploit the same representations using sparse-group LASSO regularization, enabling automatic selection of informative structural descriptors while suppressing redundant ones. Experiments on benchmark datasets show that classical centrality measures are highly competitive with learned propagation-based representations, and in several cases yield superior performance. Moreover, we observe a strong correlation between estimated NUI and downstream classification accuracy, validating NUI as an effective measure of representation utility. Overall, NetinfoGC provides a unified and interpretable framework for evaluating and exploiting graph representations without requiring end-to-end neural training.

Current approaches to enhance Large Language Model (LLM) reasoning, such as Chain-of-Thought and "Wait" prompts, primarily encourage models to think more, yet often fail to guide them toward Truth. While Representation Editing (RepE) offers a intrinsic control, its application to dynamic reasoning trajectories remains underexplored. In this work, we bridge this gap by investigating the geometry of truth within unfolding reasoning chains. We uncover three critical insights: (1) Truth is encoded at the sentence level and is entangled with latent reasoning patterns; (2) Effective intervention follows an Uncertainty Principle and a Decay Effect, requiring localization to early, high-entropy forks; (3) Naive steering vectors suffer from noise, risking collateral damage to correct trajectories. Based on these findings, we propose DynaSteer, a dynamic RepE framework. DynaSteer employs pattern clustering to disentangle reasoning manifolds and utilizes Fisher-LDA to project purified truth. By dynamically monitoring lookahead entropy, it selectively steers and rolls back trajectories only when necessary. Comprehensive experimental results on several MATH benchmark verify the effectiveness of DynaSteer, and experiments on out-of-domain coding tasks further confirm its generalization ability. Our code is publicly available at https://github.com/tianlwang/DynaSteer.

User modeling in industrial recommender systems typically produces dense embeddings, which suffer from representational constraints inherent to fixed-dimensional vectors. An emerging alternative for discrete user representation -- using LLMs to generate text-based user tokens -- captures topical co-occurrences rather than deep sequential behavior dynamics and produces outputs that are difficult to ground to item attributes. Meanwhile, Semantic ID (SID) based item tokenization has proven effective for improving generalization in generative recommendation, yet discrete SID-based representations for users remain largely unexplored. We propose TokenMinds, an industrial-scale system that extends the PLUM framework from item retrieval to user modeling, generating both discrete SID-based user tokens and dense user embeddings via an encoder-decoder architecture adapted from pre-trained LLMs. This dual-output design provides the complementary benefits of discrete, semantically grounded user representations while maintaining compatibility with existing downstream models that rely on dense embeddings. Additionally, the shared SID vocabulary naturally extends to cross-scenario modeling: by unifying long-form and short-form video behaviors into a single model, we substantially reduce training and serving costs. We validate TokenMinds through extensive offline experiments and live launches on multiple YouTube surfaces, served on full user traffic (billions of users) via an asynchronous infrastructure that decouples representation generation from downstream scoring. Focusing on ranking as the primary downstream use case, our results confirm the practical viability of SID-based user tokens at industrial scale and demonstrate that tokens and dense embeddings provide complementary value across different production ranking systems.

In this paper, we investigate the tradeoffs between compute allocation and model performance for two speech processing tasks: Automatic Speech Recognition (ASR) and Speech Emotion Recognition (SER). We propose a unified framework that analyzes three fundamental compute dimensions: model size ($x_N$), input length ($x_T$), and representation resolution ($x_V$). Motivated by recent advances in compute optimal scaling for multimodal models, we systematically vary these dimensions to examine their influence on task performance under fixed computational budgets. Our study provides insights into how compute resources can be optimally distributed across model capacity, temporal context, and representational granularity, offering practical guidelines for the design of efficient speech models. Through experiments on LibriSpeech and CREMA-D datasets, we demonstrate non-linear scaling behavior and identify optimal operating points. Our results show that (1) increasing model size yields diminishing returns: scaling Tiny (39M) to Small (244M) reduces WER by 8.22%, whereas Small to Medium (769M) reduces WER by only 2.35%; (2) an optimal audio duration of approximately 4 seconds exists for SER; and (3) reducing encoder token resolution provides an effective mechanism for lowering inference cost, Large-v3 (1540M) with 750 frames requires 2572 GFLOPS whereas with 1500 frames requires 5228 GFLOPS, with less than 3% relative increase in WER. Additionally, LoRA-based adaptation enables efficient finetuning with minimal performance degradation.

Continual learning (CL) systems often forget previously acquired knowledge, yet the mechanisms driving forgetting remain hard to isolate in practice because real datasets entangle many factors. We present a controlled, toy-world framework that makes these mechanisms observable and testable. Using a synthetic generator-separator pipeline, we define ground-truth latent features, build tasks with tunable sparsity and overlap, and introduce measurable quantities for representation strength and superposition (directional overlap among features). We then study retention dynamics-the temporal change of representation strength by fitting sparse dynamical relations (via SINDy) between retention, superposition, and exposure history. A complementary task-level analysis based on effective rank characterizes how representational capacity is allocated across tasks. Our controlled experiments yield three takeaways. (1) Superposition tends to increase over time with transient dips at task boundaries, suggesting boundary-specific interference rather than steady drift. (2) Higher feature sparsity induces more superposition yet does not inevitably cause forgetting; when representations remain strong, forgetting can be reduced despite overlap. (3) Task-level effective rank grows with sparsity, indicating broader capacity usage under sparse regimes. Together, these results nuance the common intuition that more superposition leads to more forgetting by showing that overlap interacts with representation strength and capacity allocation. Our toy analysis provides falsifiable hypotheses and diagnostic tools for CL.

Large Language Models (LLMs) and Vision-Language Models (VLMs) are increasingly evaluated on table reasoning tasks, but the role of table representation remains under-explored. In practice, the same table content may appear in different structural formats, such as HTML, Markdown, and LaTeX, or as rendered images. However, existing evaluations often let content, format, layout, and modality vary together, making it difficult to isolate representation effects. We introduce TABVERSE, a controlled multimodal table benchmark that aligns the same table content across multiple structural formats and rendered images, with question category and difficulty tags. This design enables systematic evaluation of representation effects while holding table content fixed. We evaluate LLMs and VLMs across three tasks: Question Answering (QA), Structural Understanding Capability (SUC), and Structure Reconstruction (SR). Our results show that representation choice substantially affects table understanding. Models generally perform better with structured text than with rendered images, but the size of this gap depends on the task, model, and format. HTML is often the most robust text format, while row-sensitive structural tasks and syntactically usable LaTeX reconstruction remain challenging. These findings show that table representation is a key factor in reliable table evaluation.

Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations. However, existing paired topological divergences (e.g., RTD) are limited by heuristic asymmetry and, more critically, unbounded scores that depend on sample size, hindering reliable cross-scenario benchmarking. To address these challenges, we develop a unified topological toolkit serving two complementary needs: fine-grained structural diagnosis and robust, standardized evaluation. First, we complete the RTD framework by introducing Symmetric Representation Topology Divergence (SRTD) and its efficient variant SRTD-lite. Beyond resolving the theoretical asymmetry of prior variants, SRTD consolidates diagnostic information into a single, comprehensive cross-barcode signature. This allows for precise localization of structural discrepancies and serves as an effective optimization objective without the overhead of dual directional computations. Second, to enable reliable benchmarking across heterogeneous settings, we propose Normalized Topological Similarity (NTS). By measuring the rank correlation of hierarchical merge orders, NTS yields a scale-invariant metric bounded between -1 and 1, effectively overcoming the scale and sample-dependence of unnormalized divergences. Experiments across synthetic and real-world deep learning settings demonstrate that our toolkit captures functional shifts in CNNs missed by geometric measures and robustly maps LLM genealogy even under distance saturation, offering a rigorous, topology-aware perspective that complements measures like CKA.

We develop a high-dimensional statistical theory of low-rank adaptation (LoRA) in attention models, capturing the interplay between pre-training and fine-tuning. We introduce a solvable framework in which a single-head attention layer is first pre-trained on a data-abundant task and subsequently adapted via a rank-one LoRA update on limited data. In the high-dimensional limit, both stages admit a sharp asymptotic characterization in terms of a finite set of order parameters, yielding explicit predictions for test errors and representation alignment. Our analysis shows that the impact of pre-training on LoRA is summarized by an effective noise term, from which we derive prescriptions for the optimal pre-training procedure. We also demonstrate a regime with a mismatch between the value of the test error and representation quality, and propose an application of our theory to active fine-tuning.

Knowledge benchmarks for LLMs face three issues: scaling-driven designs that do not operationalize disciplinary representativeness; flat-payment annotation that permits lazy consensus; and unaudited ranking instability under bounded test budgets. We introduce KINA, an 899-item benchmark across 261 fine-grained disciplines, with two formal results. First, we cast representativeness as a coverage-style objective over expert-elicited anchors and operationalize disciplinary representativeness through a proxy, yielding a (1-1/e) greedy approximation (Proposition 1); the guarantee applies to the proxy, not to population representativeness. Second, we prove a bonus-on-bar tournament weakly FOSD-dominates flat payment in released-review quality, with incentive-compatibility threshold B > Delta C / Delta p_min (Theorem 1). Evaluating 42 models from 13 labs, the top model, Gemini-3.1-Pro-Preview, reaches 53.17%, followed by Claude-Opus-4.6 at 49.92% and GPT-5.4 at 48.55%, leaving substantial headroom below saturation. The full leaderboard shows a tiered structure rather than a smooth total order: a small frontier tier lies above 48%, a dense strong-model tier spans roughly 38-45%, and low-performing models remain only modestly above the 10% chance baseline. Tool augmentation adds up to 5.17 points across the five tool-use evaluations, with gains varying substantially across models. We report bootstrap ranking-stability statistics to make bounded-budget variance explicit and to discourage over-interpretation of adjacent ranks.

Unified multimodal models (UMMs) aim to handle perception and generation in a single model. Yet existing UMMs still rely on a frozen, separately pretrained VAE for image generation, imposing a structural bottleneck. Naively removing it introduces a quality gap, as the model must learn both high-level structure and low-level details from raw pixels. In this paper, we propose Representation Forcing (RF), a technique that closes this gap by making representation prediction a native capability of the model. Concretely, RF forces the decoder to autoregressively predict visual representations as intermediate tokens before pixels; these tokens then stay in context to guide pixel diffusion within the same backbone. By turning representations from perception outputs into generation targets, RF eliminates the need for any external generative latent space. We find that RF benefits both understanding and generation. On image generation, our pixel-space model with RF matches state-of-the-art VAE-based unified models. On image understanding, pixel-space RF generally outperforms its VAE-based variant. Together, these results offer an effective step toward end-to-end, bottleneck-free UMMs.

Understanding how Vision-Language-Action (VLA) models transform multimodal knowledge into embodied control remains an open challenge. We present VLA-Trace, a progressive diagnostic framework that analyzes VLA models through a unified evidence chain from representation dynamics to causal control attribution and behavioral manifestation. It specifically combines cross-modal and checkpoint-drift centered kernel alignment (CKA) to trace representation evolution, attention knockout interventions to identify modality-specific control pathways, and rollout-level behavioral probes to examine grounding, shortcut dependence, and semantic following. Experiments on $π_{0.5}$ and OpenVLA reveal three key findings. First, the two models exhibit distinct modality-specific adaptation dynamics during VLA finetuning. Second, they rely on different multimodal routing strategies and layer-wise dependencies during action decoding. Third, although VLA policies excel at visually grounded trajectory generation, they remain limited in fine-grained semantic following. These findings highlight future directions for representation-preserving adaptation, causal VLA circuits, and compositional semantic control.

In real-world scenarios of linguistic steganalysis, tested texts usually come from unseen domains with different vocabularies, topics, writing styles, and steganographic generation patterns, which can significantly degrade the detection performance. Although existing cross-domain steganalysis methods can effectively alleviate this problem through distribution alignment, domain-invariant feature learning, etc., the detection performance is not satisfactory. In this paper, we propose a post-training representation editing method for cross-domain linguistic steganalysis. Specifically, the detector is first trained on source-domain data, and then the feature extractor and classifier are kept frozen, and the intermediate representations are deterministically edited before classification. For domain adaptation, we construct a domain-offset vector from marginal source and target representations. For domain generalization, we derive a source-domain cover-to-stego direction to guide sample-specific editing. Experimental results show that compared with the advanced methods, the proposed method can achieve high cross-domain detection performance, especially in terms of F1-score, while requiring no architecture modification or parameter updates after source-domain training.

Landscape feature representations play a central role in automated algorithm selection and meta-learning for black-box optimization, yet little is known about how different representations agree (or disagree) in the structures they impose on problem spaces. This paper presents a systematic unsupervised evaluation of four state-of-the-art representations (ELA, DeepELA, TransOptAS, and DoE2Vec) using a diverse set of affine combinations of BBOB functions (MA-BBOB). By applying extensive clustering analyses, coverage-based stability measures, and cross-representation similarity assessments, we show that each representation organizes the same problems in markedly different ways: ELA and TransOptAS form compact geometric structures, DeepELA provides a balanced intermediate view, and DoE2Vec achieves strong semantic alignment but with substantial fragmentation. Our results reveal that no single representation dominates; rather, they capture complementary aspects of the underlying landscapes. These findings highlight the importance of multi-view analyses for understanding representation behavior and offer guidance on selecting or combining representations in downstream meta-learning and algorithm selection tasks. In addition, across two different algorithm families (Differential Evolution and Particle Swarm Optimization), we show that landscape representations face an inherent trade-off in how well they align structural landscape descriptions with observed performance, indicating that no single representation can fully capture algorithm performance.

Korean folk painting (minhwa) is built from a small vocabulary of auspicious symbols, a tiger for protection, a pair of birds for marital harmony, a peony for wealth, that recur across many of its painted genres. This suggests an obvious computational approach, identify which symbols appear in a painting and read the genre from the inventory. Working with a public corpus that pairs whole paintings, eight-field bilingual curatorial captions, and a separate set of expert object crops, we find that this approach does not work. A model given only a list of which symbols a painting contains predicts the genre far worse than a model that fuses the image with the curatorial text, and forcing the genre representation to be object-grounded actively hurts accuracy. The visual evidence on which the genre prediction rests is nonetheless localized and inspectable. A leakage-safe object evidence map projected from a part-level detector is spatially faithful to where curators isolated symbolic objects and to a patch-based surrogate's own gradient saliency. We name this configuration a faithful-but-insufficient dissociation. The part-level explanation is honest about what the part-level model sees, yet the genre target turns on how symbols are arranged rather than on which ones appear. The same lens separates a content label that survives transfer to held-out source institutions, genre, from a style label that does not, era, a prediction we confirm on two further labels in the corpus. We release the multimodal system, a worked-example reading of one painting's evidence map against its catalogue, and a set of evaluation cautions that recur in long-tailed heritage collections.

Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such redundancy locally through Jacobian-based techniques to compute individual solutions or trajectories. While effective for solution computation, these methods do not retain a representation of the geometry of the solution set itself. In this work, we adopt a representation-centric approach to estimate the geometric structure of the solution space. We consider solution manifolds induced by general task-defining maps and construct an implicit scalar field over the configuration space, whose zero-level set corresponds to the solution manifold. To this end, we generate samples in the neighborhood of the solution manifold using a Jacobian-guided exploration strategy, which efficiently captures its local and global structure. The resulting implicit representation is defined over the configuration space and naturally induces a continuous, distance field that encodes proximity to the solution manifold. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator demonstrate the effectiveness of the proposed representation. Furthermore, the framework enables consistent modeling of solution spaces across families of tasks with continuous variation.

Speech and audio systems operate in inherently non-stationary environments, yet continual learning (CL) research in this domain, especially in the foundation model era, remains fragmented that fail to account for the coupled, geometry-sensitive nature of acoustic representations. Modern speech foundation models operate over highly entangled, continuous representations that jointly encode linguistic, speaker, and paralinguistic factors within a shared latent space. CL is therefore fundamentally about preserving and evolving shared representation structure rather than retaining isolated task knowledge. In this work, we revisit CL for speech from a representation-centered perspective, and introduce a new taxonomy that organizes CL according to how underlying representation geometry evolves under non-stationary acoustic conditions. We further identify key mismatches between current CL assumptions and speech foundation model behavior, and finally outline a set of open challenges and future research directions.

As large language models become a default source of guidance on personal, moral, and existential questions, it matters whether they draw on the religious frameworks that have historically shaped such reasoning, or systematically omit them. In this paper, we ask a deliberately narrow question: when posed an everyday ethical question for which religious perspectives may be valuable, do LLMs invoke religion at all? In contrast to benchmarks that look for the presence of political leanings or social bias, we look for the absence of religious representation as a dimension of value alignment and bias in LLMs. We term this ``omissive bias.'' To measure omissive bias, we contribute the AllFaith Religious Representation Benchmark: 150 ethically and personally salient questions, sourced from in-the-wild chat transcripts and faith-community contributors, paired with an LLM-as-judge rubric that gives full credit for any mention of a religion, a religious practice, or a religious leader. The questions are not themselves about religion--they are open-ended questions about grief, forgiveness, relationships, purpose, and honesty, where religion is one valuable perspective among several. We also run a human-subjects survey to compare LLM behavior against human expectations. Evaluating 27 models, we find that LLMs consistently underrepresent religion relative to human expectations. The omission is asymmetric: models invoke religion more readily for abstract existential questions (meaning, death, truth) than for the practical personal situations--grief, marriage, family conflict, addiction--where many people most rely on it. It is not our purpose to adjudicate which values LLMs should hold. We argue, more modestly, that current LLM responses overlook critical opportunities to reflect religious frameworks that many people draw on when navigating personal and ethical challenges.

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing ($β_c$) that, compared to the network's current state ($β$), yields a dynamic ratio $β(t)/β_c(t)$: a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, $β/β_c$ provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Parameter-efficient fine-tuning enables fast personalization of text-to-image diffusion models, but composing multiple custom concepts remains challenging due to representation interference. Existing modular methods either rely on expensive post-hoc fusion or freeze adaptation subspaces, which limit expressiveness and concept fidelity. To address this trade-off, we propose Sequential regularized LoRA (SeqLoRA), a constrained continual learning framework that jointly optimizes both LoRA factors via bilevel optimization. Theoretically, we establish strong convergence guarantees for our algorithm and model the residual layer activations as a matrix sub-Gaussian process to derive high-probability bounds on catastrophic forgetting. We further prove that learning the LoRA basis from data minimizes residual interference energy more effectively than frozen-basis methods. Experiments on multi-concept image generation demonstrate that SeqLoRA improves identity preservation and scalability across up to 101 concepts, while avoiding costly fusion and reducing attribute interference in composed generations.

Machine unlearning is a fundamental mechanism that enforces the right to be forgotten. Existing unlearning studies that rely on label manipulation or task-gradient reversal often deliver limited unlearning effectiveness. Moreover, they can undermine the original learning objective and typically do not guarantee equivalence to standard unlearning by retraining. In this paper, we propose \textbf{ManiF-SMC} (\textbf{Mani}fold \textbf{F}orgetting with \textbf{S}elf \textbf{M}ode \textbf{C}onnectivity), motivated by the observation that a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data. We begin with systematically recasting the approximate unlearning as pushing each erased sample away from its original learned manifold representation centroid toward its nearest semantic neighbors in the retained data. This reformulation aligns unlearning with retraining behavior and operates purely in representation space, reducing reliance on labels and task-specific gradients. To tackle the manifold representation-based unlearning problem, ManiF-SMC encapsulates the unlearning and representation preservation goals in a margin-based triplet loss. Because finding a suitable margin for unlearning is challenging, we propose a self-mode-connectivity module that rapidly reconstructs the local manifold to guide the adaptive margins generation for each unlearning case. Extensive experiments on four representative datasets show that ManiF-SMC achieves unlearning effectiveness comparable to state-of-the-art approximate methods while operating solely within the model's representation space.

How interpretable are the features of leading vision models? The question is increasingly pressing as these models move from research benchmarks into high-stakes deployments, yet existing methods cannot answer it reliably. We close this gap with a framework for measuring and comparing the human interpretability of vision models, built around two complementary psychophysics protocols: (1) localizability -- can an observer predict where a feature fires on a novel image? -- and (2) nameability -- can an observer accurately describe what the feature represents? Features are recovered via sparse autoencoders, and a chance-anchored scoring function places every model on a common scale. Applying the framework to six vision transformers -- two supervised ViTs and four foundation models (DINOv2, DINOv3, CLIP, SigLIP) -- we collected more than $15{,}000$ behavioral responses, analyzing the $13{,}400$ responses from the $377$ participants who passed our pre-specified quality checks. Foundation models are consistently less interpretable than their supervised counterparts, and the gap is not a capability tradeoff: interpretability does not correlate with downstream task performance on any benchmark we examine. What does correlate is the locality of a feature's activations and coarse-grained semantic alignment with humans -- models with focal activations and representations that reflect the world's broad categorical structure produce more interpretable features, whereas fine-grained perceptual alignment does not. The two protocols yield strongly correlated rankings and share the same predictors, establishing interpretability as an independent, measurable dimension of representation quality -- and, surprisingly, one on which every foundation model we tested falls below the supervised baselines that came before. Capability alone cannot close that gap; locality and coarse-grained alignment can.

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelled dataset. In the high-dimensional regime, we derive exact expressions for training and generalisation error showcasing their dependence on representation dimensionality, unlabelled and labelled sample sizes, and task alignment. Our results show that pretrained representations strongly influence downstream generalisation, and we characterize the optimal representation size as a function of task parameters: with abundant pretraining data but scarce downstream data, maximally compressed representations are optimal, whereas with limited pretraining data, higher-dimensional representations generalise better. Furthermore, we establish an exact trade-off between pretraining and supervision, quantifying how much unlabelled data is required to replace a single labelled sample. Beyond our idealised model, we observe similar phenomenology in autoencoders and pretrained LLMs. Altogether, we highlight that optimising representation size is critical, giving conditions for when compression during pretraining improves generalisation.

Single-cell perturbation modeling is fundamental for understanding and predicting cellular responses to genetic perturbations. However, existing approaches, from causal representation learning to foundation models, often struggle with an overlooked challenge: gene expression is dominated by perturbation-invariant information, while perturbation-specific signals are intrinsically sparse. As a result, learned representations either entangle invariant and perturbation-specific information, leading to spurious and non-generalizable predictors, or suppress perturbation-specific signals altogether, rendering them ineffective for prediction. To address this, we propose PerturbedVAE, a general framework designed to resolve this signal imbalance. The framework explicitly separates perturbation-specific information from dominant invariant structure and recovers causal representations to effectively utilize such information for prediction. We further provide an identifiability analysis that characterizes the conditions under which sparse perturbation effects can be reliably recovered, thereby clarifying how the framework can be concretely specified under such conditions. Empirically, PerturbedVAE achieves state-of-the-art performance on a widely used benchmark across multiple evaluation settings, yielding significant gains on out-of-distribution combinatorial predictions and uncovering interpretable perturbation-response programs.

We study behavioral alignment and representation dynamics of large language model (LLM) agents in financial decision environments. TradeArena, an auditable trading-agent testbed with risk reports, execution simulation, memory, and replayable trajectories, lets us analyze how rationales, positions, and interventions evolve under market stress. Code and data artifacts are available through the \href{https://github.com/weich97/TradeArena.git}{TradeArena repository}. We find pre-failure signatures: planning embeddings drift from normal centroids, fused plan-risk representations separate normal from pre-drawdown states, and local manifolds exhibit effective-rank contraction. Across 80 rolling failure anchors and eight LLM trajectories, this pattern persists across hash, LSA, Transformer, and white-box hidden-state probes. Stress tests with CoT-free target weights, lexical controls, OHLCV noise, and false audits show that rationale-level contraction can vanish without rationales, while intent-space and fused signatures remain informative. Structured risk feedback can act as an external alignment signal without fine-tuning, but not as a universal performance enhancer: true audit feedback improves calibration for some models, returns for others, and exposes cases where placebo or hidden feedback has higher short-horizon return but weaker alignment diagnostics. A 51-stock intraday experiment reveals a correlation blind spot: LLM rationales justify exposure to coupled assets that the risk layer clips. Finally, a financial-audit task suite shifts comparison from ``which model trades best'' to whether models can audit trajectories, respect execution boundaries, reproduce artifacts, and avoid claim overreach. These results support a research claim, not a profitability claim: auditable risk feedback and representation trajectories reveal when LLM financial reasoning is aligning, drifting, or failing.

Embedded numeric anchors on images systematically bias Vision-Language Model quality judgments across six VLMs from five architectural families (ANOVA eta^2 = 0.18-0.77, all p < 0.001). Anchor effects are 2.5x larger than severe image quality degradation, confirming bias is not reducible to visual changes. Layer-wise probing reveals consistent dissociation: layers where anchor classification saturates (L12-L34) are suboptimal for quality prediction, with optimal layers deeper (R^2 = 0.69-0.91). Fusion analysis identifies architecture-dependent integration -- instant fusion at L1-L2 in two models versus partial or no fusion in three others. These results establish a causal account of visual anchoring bias, linking behavioral susceptibility to representation dynamics.

Layer pruning efficiently reduces Large Language Model (LLM) computational costs but often triggers sudden performance collapse. Existing representation-based analyses struggle to explain this mechanism. We propose studying pruning through decision representation. Focusing on multiple-choice tasks, we introduce two metrics, Decision Margin and Option Frequency, and an Iterative Pruning method to analyze layer-wise decision dynamics. Our findings reveal a sharp decision transition that partitions the network into two stages: a Silent Phase, where the model cannot yet predict the correct answer, and a Decisive Phase, where the correct prediction emerges. We also find that pruning the Decisive Phase has minimal impact, whereas pruning the Silent Phase triggers immediate performance collapse, highlighting its extreme sensitivity to structural changes. Therefore, we conclude that pruning-induced collapse stems from disrupting the Silent Phase, which prevents the critical decision transition from occurring.

Mobile devices face diverse resource constraints and non-IID data class distributions, requiring fast on-device inference for local in-distribution (ID) classes and on-demand remote support for client-specific out-of-distribution (OOD) classes. Hybrid split federated learning (Hybrid SFL) couples personalized client-side front ends (supporting early exit) with a generalized server-side backend for fallback inference, balancing accuracy and cost. However, under client architectural heterogeneity, the existing hybrid SFL suffers from representation skew, where features from customized extractors fail to align in the shared space, leading to a sharp degradation in the server model responsible for OOD prediction. We propose HARMONY, the first hybrid SFL framework to support heterogeneous client architectures. HARMONY modifies meta-learning to simulate diverse extractors across parameters and architectures, and to learn to personalize. To mitigate representation skew, HARMONY conducts server-side contrastive learning to align extracted features, neither sacrificing clients' personalization nor sharing raw labels. Compared to the state of the art across multiple datasets and model families, HARMONY improves test accuracy by up to 43.0%/28.3% without/with OOD, respectively, while maintaining acceptable latency.

Stage-wise audio-visual encoders propagate fused intermediate states across layers, making the formation of later representations depend on the readiness of earlier fusion states. Strong local audio-visual agreement provides useful correspondence evidence, yet a fused state also needs sufficient cross-layer and cross-modal support before it can reliably guide later fusion. This paper studies this issue through propagation-aware representation readiness and formulates premature perceptual commitment as a readiness-deficiency problem, where local plausibility, propagation influence, and support insufficiency jointly appear at an intermediate stage. We propose the Delayed Perceptual Commitment Network (DPC-Net), an encoder-level framework that estimates an observable readiness-deficiency surrogate, localizes the intervention-sensitive bottleneck, and applies support-aware correction with cross-layer and cross-modal evidence. DPC-Net preserves task-specific heads, losses, decoding modules, and evaluation protocols, making it applicable to different audio-visual tasks through encoder-side intervention. Experiments on audio-visual speech separation, audio-visual event localization, and audio-visual speech recognition show consistent improvements across reconstruction, localization, and recognition regimes. Further analyses on component contribution, selection criteria, counterfactual intervention, and readiness trajectories support the effectiveness of readiness-guided bottleneck correction.

We investigate variational quantum classifiers (VQCs) for land-cover classification from multispectral satellite imagery, adopting a feature-map perspective in which the quantum circuit defines a nonlinear data embedding while the readout determines how this representation is exploited. Using the EuroSAT-MS dataset, we perform a systematic one-vs-one evaluation across all class pairs under a controlled experimental protocol, comparing classical baselines (logistic regression, SVMs, neural networks) with VQCs employing both linear readout and quantum-kernel SVM strategies. Our results show that, while VQCs with linear readout do not outperform strong classical baselines such as RBF-SVM, the same trained quantum feature map can significantly improve performance when reused within a kernel-based decision framework. A qubit-count sweep further reveals saturation effects consistent with the mismatch between exponential Hilbert space dimension and linear parameter scaling. Overall, our findings highlight that the effectiveness of quantum models depends critically on the interplay between representation and readout, and that meaningful gains may arise from combining learned quantum feature maps with classical decision mechanisms rather than seeking direct replacement of classical models.

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.

As a means to balance the growth of the AI industry with the need for privacy protection, machine unlearning plays a crucial role in realizing the ``right to be forgotten'' in artificial intelligence. This technique enables AI systems to remove the influence of specific data while preserving the rest of the learned knowledge. Although it has been actively studied, most existing unlearning methods assume that unlearning is performed only once. In this work, we evaluate existing unlearning algorithms in a more realistic scenario where unlearning is conducted repeatedly, and in this setting, we identify two critical phenomena: (1) Knowledge Erosion, where the accuracy on retain data progressively degrades over unlearning phases, and (2) Forgetting Reversal, where previously forgotten samples become recognizable again in later phases. To address these challenges, we propose SAFER (StAbility-preserving Forgetting with Effective Regularization), a continual unlearning framework that maintains representation stability for retain data while enforcing negative logit margins for forget data. Extensive experiments show that SAFER mitigates not only knowledge erosion but also forgetting reversal, achieving stable performance across multiple unlearning phases.

This paper presents FairNVT, a lightweight debiasing framework for pretrained transformer-based encoders that improves both representation and prediction level fairness while preserving task accuracy. Unlike many existing debiasing approaches that address these notions separately, we argue they are inherently connected: suppressing sensitive information at the representation level can facilitate fairer predictions. Our approach learns task-relevant and sensitive embeddings via lightweight adapters, applies calibrated Gaussian noise to the sensitive embedding, and fuses it with the task representation. Together with orthogonality constraints and fairness regularization, these components jointly reduce sensitive-attribute leakage in the learned embeddings and encourage fairer downstream predictions. The framework is compatible with a wide range of pretrained transformer encoders. Across three datasets spanning vision and language, FairNVT reduces sensitive-attribute attacker accuracy, improves demographic-parity and equalized-odds metrics, and maintains high task performance.

We introduce the Tan-HWG framework (Hebbian-Wasserstein-Geometry), a geometric theory of Hebbian plasticity in which memory states are modeled as probability measures evolving through Wasserstein minimizing movements. Hebbian learning rules are formalized as Hebbian energies satisfying a sequential stability condition, ensuring well-posed fiberwise JKO updates, optimal-transport realizations, and an energy descent inequality. This variational structure induces a fundamental separation between internal and observable dynamics. Internal memory states evolve along Wasserstein geodesics in a latent curved space, while observable quantities, such as effective synaptic weights, arise through geometric projection maps into external spaces. Simplicial projections recover classical affine schemes (including exponential moving averages and mirror descent), while revealing synaptic competition and pruning as geometric consequences of mass redistribution. Hilbertian projections provide a geometric account of phase alignment and multi-scale coherence. Classical neural networks appear as flat projections of this curved dynamics, while the framework naturally accommodates richer distributional representations, including structural weights and embedding memories, and their spectral extensions in complex internal spaces. Under mild Lipschitz regularity assumptions, including a quasi-stationary "sleep-mode" regime, we establish the existence of continuous-time limit curves. This yields a variational formulation of memory consolidation as a perturbed Wasserstein gradient flow. The framework thus provides a unified geometric foundation for synaptic plasticity, representation dynamics, and context-dependent computation.

We investigate whether graded states of mind form spectrum-like structure in transformer representation spaces. To do so, we construct a dataset of 636 short natural-language sentences annotated with both a continuous score from $-5$ to $5$ and one of seven ordered tiers, ranging from collapsed or scarcity-driven expressions to more coherent, reflective, and integrative ones. We evaluate five frozen transformer representations: four sentence-embedding models and one decoder-only residual-stream representation. Across all representations, simple probes reliably recover both the continuous score and the discrete tier labels, and permutation tests show that performance significantly exceeds shuffled-label baselines. Additional analyses reveal a consistent geometric pattern: UMAP projections show low-to-high organization, confusion matrices concentrate errors between neighboring tiers, and directional ablation identifies a prominent score-aligned component. These results suggest that transformer representations contain statistically significant, spectrum-like organization aligned with the annotated state-of-mind structure. The annotations are used only as an operational framework for representation analysis, not as a clinical or diagnostic measure.

Large language models (LLMs) often produce incorrect or outdated content after being employed. Efficient and accurate knowledge updates without costly retraining are a major challenge. This problem is particularly challenging in lifelong settings, where complex, unstructured knowledge must coexist without interference. We introduce RILKE (Representation Intervention for Lifelong KnowledgE Control), a robust and scalable method that treats knowledge control as interventions within the model's representation space. Leveraging representation-space expressiveness, we identify two key properties enabling RILKE to achieve fine-grained control over complex, unstructured knowledge while maintaining general utility with frozen base weights. During training, RILKE learns paraphrase-robust and edit-localized modules that limit each update to a low-dimensional subspace to minimize cross-edit interference. At inference, a query-adaptive router selects the appropriate module to guide the model's generation. Across LLaMA and Qwen models, RILKE scales effectively to large-scale benchmarks, demonstrating high edit success and strong paraphrase generalization while preserving general utility with modest memory overhead. These results show RILKE is an effective and scalable solution for lifelong knowledge control in LLMs.

We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (φ), we define (Q_{β,γ}(φ)=I(φ(X);Y)-β\mathcal C(φ)-γd_{\mathrm{int}}(φ)), combining task-relevant information with penalties for curvature and intrinsic latent dimension. Thus geometry becomes part of the bottleneck criterion, not only a post hoc diagnostic. Under smooth-manifold, loss-transfer, and estimator-concentration assumptions, we derive non-asymptotic low-label generalization bounds where intrinsic dimension and covering complexity enter explicitly. We characterize the information--geometry frontier and prove empirical-surrogate consistency. The analysis links encoder geometry to learning through latent covering numbers, loss-class entropy, and uniform deviation. We instantiate the theory as \texttt{V-GIB}, adding curvature and dimension penalties to variational bottleneck training. Real low-label benchmarks compare \texttt{V-GIB} with ERM, VIB, and ablations across (1%)--(20%) label fractions. Results show improved performance and reduced geometric complexity in several regimes, especially FashionMNIST and CIFAR-10, while confirming that no fixed regularizer is universally dominant.

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.