Representation Geometry in Language Models

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48 papers in the last four weeks, up 118% on the four weeks before. 0.5% of all new papers.

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Latest papers 221

Jun 2, 2026cs.AI

Decomposing how prompting steers behavior

Prompting steers large language models (LLMs) and vision-language models (VLMs) without weight updates, but it remains unclear how instruction changes reshape internal representations to produce behavior. We introduce a nested geometric decomposition framework that treats prompting as a transformation of the representational geometry of the content following the prompt. For each prompt pair, we align representations of the same stimuli under two prompts using increasingly expressive stimulus-invariant maps: translation, rigid transformation with uniform scaling, sequential axis scaling, affine transformation, and nonlinear transformation. We then causally test each map by replacing a single layer's prompt-A hidden state for held-out stimuli with its mapped counterpart and measuring recovery of prompt-B representational geometry and behavior. Across three LLMs, three VLMs, and six text or image datasets spanning style, emotion, scene content, and number, prompts consistently reshape representations toward the instructed task structure. Cross-validated variance decomposition shows that much prompt-induced activation change is captured by shape-preserving maps, especially translation and rigid transformation with uniform scaling, while tier profiles reveal model- and task-specific routing strategies across layers. Crucially, although translation and rigid tiers already improve behavioral agreement, affine transformation is the first tier to nearly recover target-prompt task geometry and yields corresponding behavioral gains. This suggests that cross-dimensional linear mixing is a key mechanism by which prompts reorganize representations toward instructed task structure. Our framework decomposes prompt-induced representational change into interpretable geometric components and reveals how models route task-relevant structure to produce prompt-driven behavior.

Fan L. Cheng, Nikolaus Kriegeskorte

Columbia University

LLM Prompting LLM Interpretability VLM Interpretability Mechanistic Interpretability Causal Interventions in Language Models Representation Geometry in Language Models

Jun 1, 2026cs.CL

Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States

Linear probing of large language model (LLM) hidden states is widely used to claim that models learn distinct representations for different reasoning types. We test this by probing Qwen3-14B on three benchmarks spanning the classical trichotomy: LogiQA 2.0 (deductive), ARC-Challenge (inductive), and

α

NLI (abductive). At layer 32 of 40, linear probes achieve 100% cross-validated accuracy with well-separated geometry (intrinsic dimensionalities: 20.6, 28.5, 33.6; convex hull contamination

\leq

1.5%). However, this separation is entirely driven by format confounds. Residualizing source identity, option count, and response length reduces accuracy to chance. Trace-anchor similarity indicates largely shared reasoning across tasks (42.5% agreement vs.\ 33.3% chance), and causal steering with random controls (

n=20

) shows no functional link between geometry and reasoning mode (

p=0.286

). Thus, high probe accuracy reflects task format rather than computational structure, motivating routine format deconfounding in mechanistic interpretability.

Subramanyam Sahoo, Vinija Jain, Aman Chadha +1

Horizon Research · Meta · Apple +1

LLM Interpretability Representation Geometry in Language Models Language Model Probing Hidden-State Probing LLM Reasoning

Jun 1, 2026cs.LG

Representational Capacity: Geometric Limits on Feature Representation in Transformer Language Models

Model dimension (

d_{model}

) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation

\varepsilon

from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high

\varepsilon

whose embeddings lack near-orthogonal structure, and models with low

\varepsilon

that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (

k/d

) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to

\varepsilon

, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

Alexander Guha

Arizona State University

Feature Superposition Transformer Expressivity Neural Representation Geometry Linear Representation Hypothesis Representation Disentanglement Representation Geometry in Language Models

Jun 1, 2026cs.CL

Geometric Latent Reasoning Induces Shorter Generations in LLMs

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Shashi Kumar, Yacouba Kaloga, Petr Motlicek +2

Idiap Research Institute, Switzerland · EPFL, Switzerland · BUT, Czech Republic

Efficient Language Model Reasoning Continuous Latent Reasoning Efficient Language Model Inference Representation Geometry in Language Models LLM Reasoning Latent Reasoning

May 31, 2026cs.CL

MENTIS: What Belief Changes Under Alignment? Measuring Multi-Scale Latent Torsion in Language Models

Preference alignment has substantially improved the observable behavior of large language models, yet it remains unclear what alignment changes internally. Aligned systems still fail under jailbreaks, prompt injection, and retrieval-time corruption, suggesting behavior-level evaluation alone is incomplete. Post-training should leave measurable traces in internal computation. We ask: when an instruction-tuned (IT) model becomes a preference-aligned (PA) model, what geometric structure changes, where do those changes concentrate, and how selectively do they vary across concepts, prompts, and model families? We introduce MENTIS, a geometry-first framework for measuring alignment-induced internal reorganization in paired checkpoints. MENTIS compares IT and PA models using a primary layerwise covariance-based torsion norm (T1), a secondary spectral torsion diagnostic (T2), and an Energy-Radiance-Activation measure (ERA) for depth localization. Across four 7-8B model pairs on LITMUS, our study reveals that alignment-induced change is selective rather than uniform: normative concepts exhibit larger torsion shifts than factual concepts on average; torsion is negatively correlated with contextual entropy; and peak effects localize to architecture-specific mid-to-late layers. The same pattern appears across word-level, prompt-level, and model-level analyses. These results suggest preference alignment leaves structured, depth-localized geometric signatures in internal computation beyond what behavior-level evaluation alone can reveal.

Partha Pratim Saha, Samarth Raina, Mayur Parvatikar +4

Pragya Lab, BITS Pilani Goa, India · IIIT Delhi, India · Amazon, USA +2

LLM Interpretability Preference Alignment Representation Geometry in Language Models

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 27, 2026cs.AI

Geometry of Human Perceptual Domains Emerges Transiently in LLM Representations

While large language models (LLMs) are trained purely on textual data, prior work has shown that their internal representations can exhibit rich geometric structure in embedding space. Building on this line of work, we investigate whether such structure is similar to human perceptual organisation across different domains (e.g., color, pitch, emotion, and taste). Specifically, we study the layer-wise emergence of intrinsic geometrical structure corresponding to perceptual modalities within the residual streams of multiple open-weight transformer architectures. Our results reveal three key findings. First, we observe the emergence of layer-wise geometric structure across multiple perceptual domains, despite the absence of any direct perceptual supervision during training. Second, these perceptual domains exhibit distinct emergence profiles, with both geometric structure and its alignment with human baselines following domain- and model-specific trajectories across depth. Third, this emergence follows a consistent representational trajectory: geometry is weak or diffuse in early layers, becomes progressively organised in intermediate layers, and is attenuated in later layers, suggesting that perceptual geometry arises transiently as part of the model's internal transformation pipeline. This provides new insight into how and where human-like perceptual geometry arises in LLMs, offering a principled pathway for mechanistic analysis of internal representations.

Simardeep Singh, Paras Chopra

Indian Institute of Technology Roorkee, Roorkee, India · Lossfunk, India

Neural Representation Geometry LLM Interpretability Representation Geometry in Language Models

May 27, 2026cs.CL

Pressure-Testing Deception Probes in LLMs: Scaling, Robustness, and the Geometry of Deceptive Representations

Linear probes trained on LLM activations are increasingly proposed as deception-detection metrics, yet report AUROC exceeding 0.96 on clean benchmarks while collapsing under distributional shift. This paper systematically pressure-tests probe-based metrics across the Gemma 3 model family (1B-27B parameters), diagnosing why they fail rather than merely documenting that they fail. We test four hypotheses about deception encoding: (1) single linear direction, (2) multi-dimensional subspace, (3) convex conic hull, (4) entropy proxy. Our design includes cross-domain transfer matrices, multi-dimensional probe analysis with permutation null baselines, entropy-residualization tests, and distractor evaluations across 8 stylistic shifts. We find that: (a) probes achieve near-perfect AUROC (>=0.998) on clean data but collapse under stylistic shifts; style-augmented probes recover near-perfect detection (mean AUROC 0.979-0.983) on unseen styles; (b) the single-direction hypothesis is rejected (k=1 captures only 0.61-0.80 AUROC), with cross-domain transfer failure confirmed as geometric rather than layer-mismatch-driven; (c) the entropy-proxy hypothesis is rejected (max |rho|=0.454, max Delta-AUROC after residualization=0.004); and (d) deception does not form a significant linear subspace (per-domain k*=0), yet multi-dimensional probes (k>=5) recover the signal through distributed sub-threshold features. Probe fragility reflects distributional narrowness rather than an architectural limitation: style-augmented probes recover near-perfect detection at both 4B and 27B, establishing that the inverse scaling pattern is a training-distribution artifact rather than a genuine scale-dependent phenomenon.

Sachin Kumar

LexisNexis, USA

LLM Evaluation Language Model Safety Evaluation LLM Interpretability Deception in Language Models Language Model Robustness Representation Geometry in Language Models+1

May 24, 2026cs.LG

Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space. Freshly introduced geometry-aware manifold methods do learn such a geometry, but require labelled class centroids together with prescribed cyclic or sequential structure. These assumptions restrict where manifold steering can be applied, since existing constructions require labelled centroids and compatible boundary conditions. We recast manifold steering more broadly as \textbf{Riemannian geodesic computation} on activation space, recovering linear and labelled-spline steering as geodesics under particular choices of metric. A principled metric within this framework is the output-space Hellinger distance pulled back to activations; we approximate this with a learned encoder trained on output distances over a small concept-token schema - no per-prompt labels, no topology prior, and no per-task curve fitting. Empirically, the method reliably drives the model onto the target class across all tasks in a standard four-task language-model arithmetic benchmark, while following more behaviourally natural trajectories than baselines on smaller output spaces. We thereby provide a unified Riemannian framework for manifold steering together with a schema-supervised, label-free instantiation that operates without labelled centroids or prescribed boundary conditions.

Narmeen Oozeer, Shivam Raval, Philip Quirke +4

Martian · Harvard University · Thoughtworks +1

Language Model Steering Representation Steering Riemannian Geometry Representation Geometry in Language Models

May 23, 2026cs.CL

Word-Class and Construction-Like Structure Emerges in Neural Successor Representations Trained on Natural Language

Neural language models are typically trained on next-token prediction, although linguistic structure spans multiple temporal scales. Successor representations (SRs) make this horizon explicit by encoding discounted distributions over future states. Here, we ask whether such predictive representations can recover not only word classes, but also finer functional and construction-like structure from natural language. A residual network trained on WikiText-103 predicts SR distributions at three horizons without part-of-speech supervision. At the shortest horizon, unsupervised clustering robustly recovers nouns, verbs, and adjectives, while directed inter-cluster transitions reproduce familiar syntactic asymmetries. At finer resolutions and across 13 part-of-speech categories, the same geometry reveals semantic-functional groupings that cross category boundaries and directed relations tracing candidate date, measurement, and title-name constructions. Part-of-speech agreement declines as the predictive horizon lengthens. These results suggest that word classes are coarse regions within a richer predictive geometry in which categorical and construction-like linguistic structure emerge from future-word distributions.

Mathis Immertreu, Achim Schilling, Thomas Kinfe +1

Cognitive Computational Neuroscience Group, Friedrich-Alexander-Universität Erlangen–Nürnberg (FAU), Germany. · Mannheim Center for Neuromodulation and Neuroprosthetics (MCNN), University Hospital Mannheim, University Heidelberg, Germany.

Predictive Representation Learning Representation Geometry in Language Models Successor Representations

May 22, 2026cs.CL

Convergence Without Understanding: When Language Models Agree on Representations but Disagree on Reasoning

Large language models trained under diverse objectives and architectures have been shown to develop increasingly similar internal representations, an observation formalized as the Platonic Representation Hypothesis. Whether this representational convergence extends to the reasoning processes that operate over shared representations remains untested. We evaluate representational similarity across 16 language models from 8 families (1.5B to 72B parameters) on 800 reasoning problems spanning mathematics, science, commonsense, and truthfulness, stratifying by problem difficulty, computational stage, and causal relevance. Our analysis reveals three dissociations: a difficulty inversion, where models converge more on problems they collectively fail (Centered Kernel Alignment [CKA] = 0.897) than on those they solve (CKA = 0.830); a generation gap, where pre-decision representations align (CKA = 0.875) while post-decision representations diverge (CKA = 0.274); and epiphenomenal correctness, where shared information is decodable across models (66% transfer accuracy) but exerts minimal causal influence on predictions (1.5% to 5.5% flip rate across ablation protocols). These results indicate that representational convergence in language models reflects shared input processing constraints rather than shared reasoning strategies, with direct implications for ensemble design, interpretability transfer, and evaluations of model similarity. Code is available at https://github.com/Usama1002/convergence-without-understanding.

Muhammad Usama, Dong Eui Chang

Control Laboratory, School of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST) Daejeon 34141, Republic of Korea · Control Laboratory, School of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST)2026 Daejeon 34141, Republic of Korea

Representational Similarity Analysis LLM Interpretability Reasoning Consistency in Language Models Representation Geometry in Language Models Platonic Representation Hypothesis LLM Reasoning

May 21, 2026cs.CL

Beyond Temperature: Hyperfitting as a Late-Stage Geometric Expansion

Recent work has identified a counterintuitive phenomenon termed "Hyperfitting", where fine-tuning Large Language Models (LLMs) to near-zero training loss on small datasets surprisingly enhances open-ended generation quality and mitigates repetition in greedy decoding. While effective, the underlying mechanism remains poorly understood, with the extremely low-entropy output distributions suggesting a potential equivalence to simple temperature scaling. In this work, we demonstrate that this phenomenon is fundamentally distinct from distribution sharpening; entropy-matched control experiments reveal that temperature scaling fails to replicate the diversity gains of hyperfitting. Furthermore, we falsify the hypothesis of static vocabulary reweighting, showing through ablation studies that hyperfitting relies on a dynamic, context-dependent rank reordering mechanism. Layer-wise analysis localizes this effect to a "Terminal Expansion" in the final transformer block, where a substantial geometric expansion of the feature space (Delta Dim approx +80.8) facilitates the promotion of deep-tail tokens. Additionally, we introduce Late-Stage LoRA, a targeted fine-tuning strategy that updates only the final 5 layers, yielding robust generation with minimal parameter updates

Meimingwei Li, Yuanhao Ding, Esteban Garces Arias +1

Department of Statistics, LMU Munich · School of Computer and Information Engineering, Henan University · Munich Center for Machine Learning (MCML)

LLM Interpretability LLM Fine-Tuning Diverse Text Generation Representation Geometry in Language Models

May 19, 2026cs.LG

Reading Calibrated Uncertainty from Language Model Trajectories

The maximum softmax probability (MSP) represents a default approach when evaluating uncertainty quantification for language model generation with structured output. Although cheap, it is often miscalibrated. Methods that probe the model's internal activations feed raw hidden states into opaque classifiers, reading activations as static snapshots and leaving implicit the layer-wise trajectory by which a representation is formed. Yet, similar endpoints can arise from very different paths, and how evidence accumulates, reinforces, or reverses across depth might reveal uncertainty that final probabilities obscure. We extract eleven scale-invariant geometric features, tracing the cumulative path of per-layer MLP updates, and feed them to a sparse linear probe. The probe outperforms MSP under selective abstention, with gains scaling with baseline miscalibration up to 21 AURC points. Because every feature has a closed-form geometric meaning, the probe's coefficients trace how and where along depth errors take shape -- which layers commit prematurely, which contradict the running state, where trajectories drift away from their endpoint.

Aliai Eusebi, Alexander Herzog, Xiaoyu Liang +3

University College London, London, United Kingdom · Core46, London, United Kingdom

Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Representation Geometry in Language Models Uncertainty Calibration Language Model Probing

May 16, 2026cs.CL

Large language models reorganize representational geometry during in-context learning

Large language models (LLMs) exhibit remarkable flexibility: they can adapt to novel tasks from in-context examples without any parameter updates, a capability known as in-context learning (ICL). Prior work on synthetic tasks has shown that ICL can implement specific algorithms, demonstrating architectural competence, and mechanistic analyses have identified key circuits that support this behavior. However, because in-context computation -- regardless of its algorithmic form -- relies on transformations in high-dimensional representation space, it remains unclear how the geometry of that space shapes ICL effectiveness. Motivated by the neuroscience view of classification as the untangling of neural representations, we hypothesize that ICL depends on the successful online untangling of task-relevant representations. To test this idea, we study how LLMs classify in-context examples whose labels are defined by the model's own internal representations with known structure. We show that ICL performance correlates systematically with the representational structure of the underlying classification task and that successful ICL is accompanied by geometric reorganization that increases online separability. We further find that LLM behavior is well described by a prototype-like algorithm that integrates evidence while reshaping representations to support classification. These findings offer a geometric account of ICL in pretrained LLMs, establish representational geometry as a mechanistic constraint on ICL, and quantify the gap between what pretrained representations afford and what in-context learning can exploit.

Hua-Dong Xiong, Li Ji-An, Robert C. Wilson +2

School of Psychological and Brain Sciences, Georgia Tech · Department of Psychology, New York University · School of Psychological and Brain Sciences, Georgia Tech 3 Center of Excellence for Computational Cognition, Georgia Tech +2

Neural Representation Geometry Representation Disentanglement In-Context Learning Representation Geometry in Language Models

May 16, 2026cs.LG

Scale Determines Whether Language Models Organize Representation Geometry for Prediction

In language models, what a representation encodes is determined by the geometry of its representation space: distances, not activations, carry meaning. Existing tools characterize the shape of this geometry but do not ask what that shape is organized for. We introduce Subspace PGA, a metric that tests whether a layer's distance structure aligns with the readout subspace of the unembedding matrix

W_U

more than with random subspaces of equal size. Across seven Pythia models (70M--6.9B) and three cross-family models, intermediate geometry is significantly organized for prediction (peak

z = 9

--

24

), but the degree is scale-dependent: small models (

d \leq 1024

) progressively lose it at late layers during training -- even as loss keeps improving -- while large models (

d \geq 2048

) preserve it throughout. We trace this to a capacity trade-off: a few dominant directions migrate away from

W_U

's readout, masking rather than destroying the predictive structure beneath, and removing them restores alignment. Neither spectral metrics nor loss curves capture this distinction. Scale thus determines not only how well a model predicts, but how its representation geometry is organized to do so.

Weilun Xu

School of Computer and Communication Sciences ´Ecole Polytechnique F´ed´erale de Lausanne

Language Model Pretraining Neural Representation Geometry Language Model Scaling Representation Geometry in Language Models

May 14, 2026cs.CL

Reasoning Models Don't Just Think Longer, They Move Differently

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Anders Gjølbye, Lars Kai Hansen, Sanmi Koyejo

Technical University of Denmark · Stanford University

LLM Interpretability Representation Geometry in Language Models Algorithmic Reasoning LLM Reasoning Large Reasoning Models Reasoning Trace Analysis

May 14, 2026cs.LG

Representation Without Reward: A JEPA Audit for LLM Fine-Tuning

Joint-embedding predictive architectures (JEPAs) propose that a model should learn more useful abstractions when trained to predict latent representations rather than observed outputs. For autoregressive language-model fine-tuning the principle entails a stricter requirement: the induced hidden-state geometry must reach the language-model head \emph{and} improve the decoded task metric. We test that requirement under a fixed Llama-3.2-1B-Instruct LoRA harness on natural-language-to-regex generation, comparing twenty-two training-time auxiliaries across trajectory-shape regularisation, distributional constraints, predictor/target asymmetry, Fisher-metric Jacobi residuals, and a decoder-visible JEPA objective constructed to lie in cross-entropy's positive cone. The empirical answer is a structured null: several auxiliaries clear single-cell paired

α= 0.10

without correction (T3-Local at

Δ= +2.53

~pp,

p = 0.003

being the strongest), but none survives Bonferroni or Holm--Bonferroni at the relevant family-wise threshold, even though many change curvature, anisotropy, variance, and gradient direction. Decoder-visible JEPA yields the first positive auxiliary--cross-entropy gradient cosine in the study, yet exact match remains inside seed noise; a full-fine-tuning replication of the same auxiliary at

n = 5

seeds reproduces the null on both benchmarks (TURK:

Δ= +0.04

~pp,

p_{\text{paired}} = 0.96

; SYNTH:

Δ= +0.52

~pp,

p_{\text{paired}} = 0.28

), so the null is robust across LoRA and full fine-tuning for the decoder-visible construction. Hidden-state representation work and decoded-task accuracy are therefore weakly coupled in this regime; we accordingly reframe LLM-domain JEPA evaluation as a coupling problem, in which the operative question is under which metrics useful hidden geometry becomes decoder-visible task signal.

Biswa Sengupta

LLM Suite Team, JPMorgan Chase & Co.

LLM Auditing LLM Fine-Tuning Joint-Embedding Predictive Architecture Representation Geometry in Language Models

May 13, 2026cs.CL

Tracing Persona Vectors Through LLM Pretraining

How large language models internally represent high-level behaviors is a core interpretability question with direct relevance to AI safety: it determines what we can detect, audit, or intervene on. Recent work has shown that traits such as evil or sycophancy correspond to linear directions in the internal activations, the so-called persona vectors. Although these vectors are now routinely utilized to inspect and steer model behavior in safety-relevant settings, how these representations are formed during training remains unknown. To address this gap, we trace persona vectors across the pretraining of OLMo-3-7B, finding that persona vectors form remarkably early -- within 0.22% of OLMo-3 pretraining -- and remain effective for steering the fully post-trained instruct models. Although core representations are formed early on, persona vectors continue to refine geometrically and semantically throughout pretraining. We further compare alternative elicitation strategies and find that all yield effective directions, with each strategy surfacing qualitatively distinct facets of the underlying persona. Replicating our analysis on Apertus-8B reveals that our findings transfer qualitatively beyond OLMo-3. Our results establish persona representations as stable features of early pretraining and open a path to studying how training forms, refines, and shapes them.

Viktor Moskvoretskii, Dominik Glandorf, Jorge Medina Moreira +2

EPFL

Language Model Pretraining LLM Interpretability Personality Modeling in Language Models Representation Geometry in Language Models Activation Steering

May 12, 2026cs.LG

Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs

Hidden states change substantially across the layers of modern language models, but most layer-wise analyses focus on one aspect of that change. We propose Layer-wise Representation Dynamics (LRD), a framework with three layer-wise measurement families: Frenet (Grassmann speed and curvature) for global subspace motion, Neighborhood Retention Score (NRS) for local nearest-neighbor retention, and Graph Filtration Mutual Information (GFMI) for alignment with the final layer. Applying LRD to 31 models (encoder-based and decoder-based embedders, plus base LLMs) on 30 MTEB tasks reveals architectural and task-level differences that are not apparent from final-layer representations alone. We then use LRD for two applications: label-free model selection and inference-time layer pruning. For selection, all three model-level scores correlate positively with downstream MTEB performance, with end-to-end subspace displacement (d_{0,L}) the strongest, and the same direction holds on a smaller base-LLM MMLU panel. For pruning, GFMI is the only measurement-guided rule that beats Random at the 15% and 20% budgets and has the best median change at every budget. Frenet is effective only at the lightest budget, while NRS does not transfer from model selection to pruning. These results show that layer-wise structure provides signal for both interpretation and deployment decisions.

Jingzhou Jiang, Yi Yang, Kar Yan Tam

The Hong Kong University of Science and Technology

Text Embeddings LLM Pruning Representation Learning LLM Interpretability Text Embedding Models Representation Geometry in Language Models

May 12, 2026cs.CL

Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space

Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.

Eric Bigelow, Raphaël Sarfati, Daniel Wurgaft +5

LLM Interpretability In-Context Learning Belief Updating in LLMs Representation Geometry in Language Models

May 10, 2026cs.CL

Beyond Language: Format-Agnostic Reasoning Subspaces in Large Language Models

Large language models represent the same reasoning in vastly different surface forms -- English prose, Python code, mathematical notation -- yet whether they share a common internal substrate across these symbolic systems remains unknown. We introduce the TriForm Benchmark (18 concepts x 6 forms x 3 instances = 324 stimuli) and study five LLMs (1.6B-8B) across three architecture families. Using permutation-corrected RSA, cross-form probing, and activation patching, we find converging evidence for a Format-Agnostic Reasoning Subspace (FARS) in middle layers. We make FARS concrete: concept-centroid PCA extracts a 10-dimensional subspace that amplifies concept structure 3x while suppressing form information to near zero. Replacing only these 10 dimensions during cross-form patching preserves 90-96% of model output -- far exceeding both full activation replacement (44-56%) and variance-maximizing PCA (60-74%) -- while ablating them causes targeted disruption. FARS generalizes to held-out concepts and converges across architectures (CCA > 0.79 for all model pairs), providing within-modality evidence for the Platonic Representation Hypothesis. We further discover a declarative-procedural asymmetry: representations are far more compatible between prose and mathematics than between either and code, suggesting that the critical axis of divergence is not linguistic vs. formal but declarative vs. procedural.

Aojie Yuan, Zhiyuan Su

University of Southern California · 2Duke University

LLM Interpretability Representation Geometry in Language Models Representation Alignment Platonic Representation Hypothesis Language Model Probing

May 8, 2026cs.CL

Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative

Mean-pooled cosine similarity is the default metric for comparing neural representations across languages, modalities, and tasks. We establish that this metric is not length-invariant: under the anisotropy that characterizes modern transformer representations, mean-pooled cosine grows monotonically in sequence length, independent of representational content. Empirically, on HumanEvalPack across four code LLMs, the length ratio alone explains

R^2 = 0.52

--

0.75

of cross-language "Python proximity," while AST depth and shared-token fraction add less than 3% of explained variance beyond length. Substituting Centered Kernel Alignment (CKA) reduces explained variance by 83% and reverses the sign of the length coefficient (

β_{\mathrm{len}}: +0.86 \to -0.37

). The same pattern holds in Mistral-7B on parallel WMT pairs (

R^2 = 0.23

EN-FR,

R^2 = 0.33

EN-DE for cosine;

R^2 < 0.01

for CKA). In CLIP ViT-B/32, mean-pooling reduces the length effect relative to EOS-pooling (

R^2: 0.21 \to {<}0.01

), as predicted by the theory's dependence on anisotropy. We argue that length-invariant metrics such as CKA should be the default for cross-representation comparisons, and that recent claims of cross-lingual representational convergence built on mean-pooled cosine warrant re-examination.

Sibayan Mitra, Dhruv Kumar

BITS Pilani · Birla Institute of Technology and Science, Pilani, India.

Neural Representation Geometry Representation Geometry in Language Models

May 7, 2026cs.LG

Don't Retrain, Align: Adapting Autoregressive LMs to Diffusion LMs via Representation Alignment

Diffusion language models (DLMs) have recently demonstrated capabilities that complement standard autoregressive (AR) models, particularly in non-sequential generation and bidirectional editing. Although recent work has shown that pretrained autoregressive checkpoints can be converted into diffusion language models, existing recipes primarily transfer parameters through continued denoising training with objective- and attention-level modifications. We instead ask whether the internal representation geometry learned by next-token prediction can be explicitly preserved during AR-to-DLM conversion. We hypothesize that much of the semantic structure learned by AR pretraining can transfer across generation orders, and thus DLM training should be viewed as relearning the decoding path rather than relearning language representations. To investigate this, we introduce REPR-ALIGN, a representation alignment objective that adapts a bidirectional masked diffusion model to reuse representations from a pretrained AR model of identical architecture. Concretely, we align the hidden states of the DLM to the frozen AR model at every layer using cosine similarity, while optimizing the standard masked denoising objective. This simple alignment, with no adapters and no architectural changes beyond the attention mask, yields up to 4x training acceleration in our setting and is particularly effective in low-data regimes. Our results suggest that linguistic representations can transfer across generation order, and that representation alignment provides a simple and effective technique for training diffusion language models. Code is available at https://github.com/pengzhangzhi/Open-dLLM.

Fred Zhangzhi Peng, Alexis Fox, Anru R. Zhang +1

Duke University · AITHYRA

Masked Diffusion Models Diffusion Language Models Representation Geometry in Language Models Representation Alignment

May 7, 2026cs.LG

Invariant Features in Language Models: Geometric Characterization and Model Attribution

Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local geometric framework in which semantically equivalent inputs occupy structured regions in latent space, with paraphrastic variation along nuisance directions and semantic identity preserved in invariant subspaces. Building on this view, we make three contributions: (1) a geometric characterization of invariant latent features, (2) a contrastive subspace discovery method that separates semantic-changing from semantic-preserving variation, and (3) an application of invariant representations to zero-shot model attribution. Across models and layers, empirical results support these contributions. Invariant structure emerges in specific depth regions, semantic displacement lies largely outside the nuisance subspace, and representation-level interventions indicate a causal role of invariant components in model outputs. Invariant representations also capture model-specific geometric patterns, enabling accurate attribution. These findings suggest that semantic invariance can be viewed as a local geometric property of latent representations, offering a principled perspective on how language models organize meaning.

Agnibh Dasgupta, Abdullah Tanvir, Xin Zhong

Department of Computer Science University of Nebraska Omaha, Omaha, NE, USA

Neural Representation Geometry Invariant Representation Learning Representation Geometry in Language Models

May 6, 2026cs.LG

A geometric relation of the error introduced by sampling a language model's output distribution to its internal state

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an

\mathfrak{so}(n)

-valued 1-form that depends only on the geometry of the token embeddings. Despite this purely geometric origin, we show that its curvature is semantically meaningful: On chess reasoning tasks, the curvature couples to the world model of an off-the-shelf instruction-tuned model, with transformations clustering by board region and respecting piece importance. Our findings suggest that token space geometry directly reflects how models internally represent problems.

Albert F. Modenbach

Department of Mathematics, King’s College London, United Kingdom.

Neural Representation Geometry LLM Interpretability Representation Geometry in Language Models

May 5, 2026cs.LG

The Right Answer, the Wrong Direction: Why Transformers Fail at Counting and How to Fix It

Large language models often fail at simple counting tasks, even when items to count are in the prompt. We investigate whether this failure occurs because transformers do not represent counts internally, or because they cannot convert representations to the correct output tokens. Across three model families: Pythia, Qwen3, and Mistral, ranging from 0.4B to 14B parameters, we find evidence for the second explanation. Linear probes recover the correct count from intermediate layers with

R^2>0.99

, showing that the information is present. However, the internal directions that encode counts are nearly orthogonal to digit-token output-head rows (

|\cos| \leq 0.032

). In other words, the model stores the count in a form that the digit logits do not naturally read out. We localize this failure with two interventions. Updating only the digit rows of the output head (36,864 parameters) substantially improves constrained digit prediction (60.7--100.0% on four tasks), but it does not fix unconstrained generation (0%); we do not claim that digit-row repair fixes open-ended text. By contrast, small LoRA on attention Q/V (7.67M parameters) improves upstream routing and achieves 83.1%

\pm

7.2% in true greedy autoregressive generation (deployable fix). Logit-lens at layer 35 (entity counting; correct-digit rank): (i) median over 3 seeds drops from order-

10^4

to 1; (ii) seed 42 shows

54{,}332 \to 838

(median top-1 while one seed stays far below). Norm, logit-lens, and cross-task analyses generalize the bottleneck to counting, addition, and list length; nulls on MMLU and GSM8K and limited DROP transfer. These results identify counting failure as a geometric readout bottleneck, not an internal-representation failure: the model knows the count but the output pathway is misaligned with tokens needed to express it.

Gabriel Garcia

Independent Researcher

Numerical Reasoning in Language Models Transformer Interpretability LLM Fine-Tuning Object Counting Language Modeling Representation Geometry in Language Models

May 4, 2026cs.CL

Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability

A reliable language model should be able to signal, prior to generation, when a query falls outside its knowledge. We investigate whether representation geometry can provide such a pre-generation signal by measuring the deviation of hidden states from an answerable reference set, requiring no labeled failure data and no access to model outputs. Across three instruction-tuned models (Llama 3.1-8B, Qwen 2.5-7B, and Mistral-7B-Instruct) and three prompt forms (Math, Fact, Code), we find that geometry primarily encodes task form. Within mathematical prompts, unanswerable inputs consistently deviate from the answerable centroid, yielding strong separation (ROC-AUC 0.78-0.84). This single-pass pre-generation signal outperforms a simple refusal baseline and compares favorably to self-consistency. It also captures cases where models do not explicitly refuse. In contrast, no reliable geometric signal emerges for factual prompts, indicating that the effect is form-conditional rather than universal. Code prompts show large effect sizes with higher variance, suggesting partial generalization beyond mathematical form. A layer-wise analysis reveals that the signal arises in early layers and gradually attenuates toward the output. These results suggest that answerability-related geometry is established before the final stages of generation. Together, these findings indicate that geometric deviation can serve as a lightweight pre-generation signal that is reliable in structured domains with formal answerability constraints, with clear boundaries on where it generalizes.

Yucheng Du

University of Southern California

Representation Geometry LLM Reliability LLM Uncertainty Estimation Representation Geometry in Language Models Language Model Probing

May 3, 2026cs.CL

The Cylindrical Representation Hypothesis for Language Model Steering

Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH assumes that concepts can be orthogonalized for lossless control, this idealized mapping fails in real representations and cannot account for the observed unpredictability of steering. By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH). In CRH, a central axis captures the main difference between concept absence and presence and drives concept generation. A surrounding normal plane controls steering sensitivity by determining how easily the axis can activate the target concept. Within this plane, only specific sensitive sectors strongly facilitate concept activation, while other sectors can suppress or delay it. While the surrounding normal plane can be reliably identified from difference vectors, the sensitive sector cannot, introducing intrinsic uncertainty at the sector level. This uncertainty provides a principled explanation for why steering outcomes often fluctuate even when using well-aligned directions. Our experiments verify the existence of the cylindrical structure and demonstrate that CRH provides a valid and practical way to interpret model steering behavior in real settings: https://github.com/mbzuai-nlp/CRH.

Lang Gao, Jinghui Zhang, Wei Liu +7

Department of Natural Language Processing, Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · Department of Computer Science, National University of Singapore, Singapore

Language Model Steering LLM Interpretability Linear Representation Hypothesis Representation Steering Representation Geometry in Language Models

May 3, 2026cs.LG

Probe-Geometry Alignment: Erasing the Cross-Sequence Memorization Signature Below Chance

Recent attacks show that behavioural unlearning of large language models leaves internal traces recoverable by adversarial probes. We characterise where this retention lives and show it can be surgically removed without measurable capability cost. Our central protocol is a leave-one-out cross-sequence probe that tests whether a memorisation signature generalises across held-out sequences. The signature is real and consistent across scale: memorisation-specific gaps of +0.32, +0.19, +0.30 on Pythia-70M, GPT-2 medium, and Mistral-7B; on Pythia-70M, the random-initialisation control collapses to -0.04 at the deepest layer where the pretrained signature peaks. The probe direction is causally separable from recall -- projecting it out collapses the signature locally (+0.44 -> -0.19) while behavioural recall barely changes -- and a probe trained on naturally memorised content does not classify fine-tuning-injected secrets, marking two representationally distinct regimes. We then introduce probe-geometry alignment (PGA), a surgical erasure that aligns activations along the probe's live readout direction at each depth. PGA drives the cross-sequence probe below random chance at all four scales tested (toy depth-4: 0.17; Pythia-70M: 0.07; Mistral-7B: 0.45; GPT-2 medium: 0.06 via MD-PGA k=2) and remains robust to six adversarial probe variants. Against a re-fitting attacker who trains a fresh probe on PGA-treated activations, we extend PGA adversarially, defeating the re-fit probe at every memorisation-relevant depth while preserving five zero-shot capability benchmarks within 2.8 percentage points per task (mean Δacc = +0.2pp). The cross-sequence signature is a real, causally separable, regime-specific property of pretrained representations -- removable below chance with a single rank-one intervention per depth at no measurable capability cost.

Anamika Paul Rupa, Anietie Andy

Howard University

Memorization in Language Models Neural Network Memorization Persistent Memory for Language Models LLM Memory Privacy Leakage in Language Models Memorization in Generative Models+4

May 2, 2026cs.LG

Reasoning emerges from constrained inference manifolds in large language models

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference. We find that inference-time dynamics consistently self-organize into low-dimensional manifolds embedded within high-dimensional representation spaces. we find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning. Instead, effective reasoning dynamics emerge within a constrained structural regime characterized by three conditions: adequate representational expressivity, spontaneous manifold compression, and preservation of non-degenerate information volume within the compressed subspace. Models outside this regime exhibit characteristic pathological inference dynamics. Based on these insights, we introduce a unified, label-free diagnostic computed solely from internal dynamics. These findings suggest that reasoning in LLMs is fundamentally governed by geometric and informational constraints, offering a complementary framework to benchmark-centric assessment.

Yanbiao Ma, Fei Luo, Linfeng Zhang +10

Renmin University of China · Tsinghua University · Xiaomi EV +1

LLM Inference LLM Interpretability Representation Geometry in Language Models LLM Reasoning