Representation Geometry in Language Models

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Decomposing how prompting steers behavior
Jun 2, 2026Fan L. Cheng, Nikolaus KriegeskorteLLM Prompting LLM Interpretability
Columbia University
Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States
Jun 1, 2026Subramanyam Sahoo, Vinija Jain, Aman Chadha +1LLM Interpretability Representation Geometry in Language Models
Horizon Research · Meta · Apple +1
Representational Capacity: Geometric Limits on Feature Representation in Transformer Language Models
Jun 1, 2026Alexander GuhaFeature Superposition Transformer Expressivity
Arizona State University
Geometric Latent Reasoning Induces Shorter Generations in LLMs
Jun 1, 2026Shashi Kumar, Yacouba Kaloga, Petr Motlicek +2Efficient Language Model Reasoning Continuous Latent Reasoning
Idiap Research Institute, Switzerland · EPFL, Switzerland · BUT, Czech Republic
MENTIS: What Belief Changes Under Alignment? Measuring Multi-Scale Latent Torsion in Language Models
May 31, 2026Partha Pratim Saha, Samarth Raina, Mayur Parvatikar +4LLM Interpretability Preference Alignment
Pragya Lab, BITS Pilani Goa, India · IIIT Delhi, India · Amazon, USA +2
Representation Collapse in Sequential Post-Training of Large Language Models
May 28, 2026Yichen Liu, Mingyu Chen, Hao Wang +7Continual Learning for LLMs Representation Collapse
Hangzhou Dianzi University · Zhejiang Gongshang University · Ningbo University +1
Geometry of Human Perceptual Domains Emerges Transiently in LLM Representations
May 27, 2026Simardeep Singh, Paras ChopraNeural Representation Geometry LLM Interpretability
Indian Institute of Technology Roorkee, Roorkee, India · Lossfunk, India
Pressure-Testing Deception Probes in LLMs: Scaling, Robustness, and the Geometry of Deceptive Representations
May 27, 2026Sachin KumarLLM Evaluation Language Model Safety Evaluation
LexisNexis, USA
Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering
May 24, 2026Narmeen Oozeer, Shivam Raval, Philip Quirke +4Language Model Steering Representation Steering
Martian · Harvard University · Thoughtworks +1
Word-Class and Construction-Like Structure Emerges in Neural Successor Representations Trained on Natural Language
May 23, 2026Mathis Immertreu, Achim Schilling, Thomas Kinfe +1Predictive Representation Learning Representation Geometry in Language Models
Cognitive Computational Neuroscience Group, Friedrich-Alexander-Universität Erlangen–Nürnberg (FAU), Germany. · Mannheim Center for Neuromodulation and Neuroprosthetics (MCNN), University Hospital Mannheim, University Heidelberg, Germany.
Convergence Without Understanding: When Language Models Agree on Representations but Disagree on Reasoning
May 22, 2026Muhammad Usama, Dong Eui ChangRepresentational Similarity Analysis LLM Interpretability
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
Beyond Temperature: Hyperfitting as a Late-Stage Geometric Expansion
May 21, 2026Meimingwei Li, Yuanhao Ding, Esteban Garces Arias +1LLM Interpretability LLM Fine-Tuning
Department of Statistics, LMU Munich · School of Computer and Information Engineering, Henan University · Munich Center for Machine Learning (MCML)
Reading Calibrated Uncertainty from Language Model Trajectories
May 19, 2026Aliai Eusebi, Alexander Herzog, Xiaoyu Liang +3Confidence Estimation in Language Models LLM Reliability
University College London, London, United Kingdom · Core46, London, United Kingdom
Large language models reorganize representational geometry during in-context learning
May 16, 2026Hua-Dong Xiong, Li Ji-An, Robert C. Wilson +2Neural Representation Geometry Representation Disentanglement
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
Scale Determines Whether Language Models Organize Representation Geometry for Prediction
May 16, 2026Weilun XuLanguage Model Pretraining Neural Representation Geometry
School of Computer and Communication Sciences ´Ecole Polytechnique F´ed´erale de Lausanne
Reasoning Models Don't Just Think Longer, They Move Differently
May 14, 2026Anders Gjølbye, Lars Kai Hansen, Sanmi KoyejoLLM Interpretability Representation Geometry in Language Models
Technical University of Denmark · Stanford University
Representation Without Reward: A JEPA Audit for LLM Fine-Tuning
May 14, 2026Biswa SenguptaLLM Auditing LLM Fine-Tuning
LLM Suite Team, JPMorgan Chase & Co.
Tracing Persona Vectors Through LLM Pretraining
May 13, 2026Viktor Moskvoretskii, Dominik Glandorf, Jorge Medina Moreira +2Language Model Pretraining LLM Interpretability
EPFL
Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs
May 12, 2026Jingzhou Jiang, Yi Yang, Kar Yan TamText Embeddings LLM Pruning
The Hong Kong University of Science and Technology
Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space
May 12, 2026Eric Bigelow, Raphaël Sarfati, Daniel Wurgaft +5LLM Interpretability In-Context Learning
Beyond Language: Format-Agnostic Reasoning Subspaces in Large Language Models
May 10, 2026Aojie Yuan, Zhiyuan SuLLM Interpretability Representation Geometry in Language Models
University of Southern California · 2Duke University
Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative
May 8, 2026Sibayan Mitra, Dhruv KumarNeural Representation Geometry Representation Geometry in Language Models
BITS Pilani · Birla Institute of Technology and Science, Pilani, India.
Don't Retrain, Align: Adapting Autoregressive LMs to Diffusion LMs via Representation Alignment
May 7, 2026Fred Zhangzhi Peng, Alexis Fox, Anru R. Zhang +1Masked Diffusion Models Diffusion Language Models
Duke University · AITHYRA
Invariant Features in Language Models: Geometric Characterization and Model Attribution
May 7, 2026Agnibh Dasgupta, Abdullah Tanvir, Xin ZhongNeural Representation Geometry Invariant Representation Learning
Department of Computer Science University of Nebraska Omaha, Omaha, NE, USA
A geometric relation of the error introduced by sampling a language model's output distribution to its internal state
May 6, 2026Albert F. ModenbachNeural Representation Geometry LLM Interpretability
Department of Mathematics, King’s College London, United Kingdom.
The Right Answer, the Wrong Direction: Why Transformers Fail at Counting and How to Fix It
May 5, 2026Gabriel GarciaNumerical Reasoning in Language Models Transformer Interpretability
Independent Researcher
Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability
May 4, 2026Yucheng DuRepresentation Geometry LLM Reliability
University of Southern California
The Cylindrical Representation Hypothesis for Language Model Steering
May 3, 2026Lang Gao, Jinghui Zhang, Wei Liu +7Language Model Steering LLM Interpretability
Department of Natural Language Processing, Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · Department of Computer Science, National University of Singapore, Singapore
Probe-Geometry Alignment: Erasing the Cross-Sequence Memorization Signature Below Chance
May 3, 2026Anamika Paul Rupa, Anietie AndyMemorization in Language Models Neural Network Memorization
Howard University
Reasoning emerges from constrained inference manifolds in large language models
May 2, 2026Yanbiao Ma, Fei Luo, Linfeng Zhang +10LLM Inference LLM Interpretability
Renmin University of China · Tsinghua University · Xiaomi EV +1

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Decomposing how prompting steers 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

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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.

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Latest papers 221