Representation Geometry in Language Models

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This field studies the shapes and relationships formed by token embeddings and hidden activations, and how those structures change across layers, contexts, and training. Researchers use linear probes, representational similarity analysis, spectral and manifold methods, sparse autoencoders, and causal interventions such as activation patching and steering. These tools are applied to questions about reasoning, multilingual transfer, retrieval, safety, and reliability, using settings that range from controlled synthetic tasks to benchmarks such as GSM8K and MTEB. A central open tension is that information being decodable or geometrically similar does not guarantee that a model uses it causally; useful structure may also be local, nonlinear, or sensitive to measurement choices.

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417 papers78 papers in the last four weeks, up 34% on the four weeks before. 0.5% of all new papers.

A Gauge Theory of Superposition: Toward a Sheaf-Theoretic Atlas of Neural Representations
Feb 28, 2026Hossein JavidniaLLM Interpretability Representation Geometry in Language Models
School of Computing, Dublin City University, Ireland
Universal Conceptual Structure in Neural Translation: Probing NLLB-200's Multilingual Geometry
Feb 27, 2026Kyle Elliott MathewsonMultilingual Language Models Representation Geometry in Language Models
University of Alberta
Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA
Feb 26, 2026Hai Huang, Yann LeCun, Randall BalestrieroEfficient Language Model Training LLM Training
Atlassian · NYU · Brown
Causality $\neq$ Invariance: Function and Concept Vectors in LLMs
Feb 25, 2026Gustaw Opiełka, Hannes Rosenbusch, Claire E. StevensonRepresentation Geometry in Language Models In-Context Learning
University of Amsterdam
Structure and Redundancy in Large Language Models: A Spectral Study via Random Matrix Theory
Feb 25, 2026Davide EttoriLLM Compression Representation Geometry in Language Models
How Transformers Reject Wrong Answers: Rotational Dynamics of Factual Constraint Processing
Feb 25, 2026Javier MarínTransformer Interpretability LLM Interpretability
Groundlens-dev
Frayed RoPE and Long Inputs: A Geometric Perspective
Feb 24, 2026Davis Wertheimer, Aozhong Zhang, Derrick Liu +2Rotary Positional Embeddings Long-Context Language Modeling
IBM Research · University at Albany, SUNY
Emergent Manifold Separability during Reasoning in Large Language Models
Feb 23, 2026Chanwoo Chun, Alexandre Polo, SueYeon ChungRepresentation Geometry in Language Models CoT Reasoning
Department of Physics, Harvard University · Center for Data Science, New York University · Kempner Institute, Harvard University +1
On the Semantic and Syntactic Information Encoded in Proto-Tokens for One-Step Text Reconstruction
Feb 20, 2026Ivan Bondarenko, Egor Palkin, Fedor TikunovNon-Autoregressive Text Generation Representation Geometry in Language Models
Understanding Unreliability of Steering Vectors in Language Models: Geometric Predictors and the Limits of Linear Approximations
Feb 19, 2026Joschka BraunLanguage Model Steering Activation Steering
Eberhard Karls University of Tübingen Faculty of Science
ADAPT: Hybrid Prompt Optimization for LLM Feature Visualization
Feb 19, 2026João N. Cardoso, Arlindo L. Oliveira, Bruno MartinsLLM Interpretability Prompt Optimization
Instituto Superior T´ecnico · INESC-ID
Mechanistic Interpretability of Cognitive Complexity in LLMs via Linear Probing using Bloom's Taxonomy
Feb 19, 2026Bianca Raimondi, Maurizio GabbrielliLLM Interpretability Representation Geometry in Language Models
Department of Computer Science and Engineering, University of Bologna, Bologna, Italy
The Geometric Anatomy of Capability Acquisition in Transformers
Feb 17, 2026Jayadev BillaRepresentation Geometry in Language Models Representation Collapse
San Jose, CA, USA
Recursive Concept Evolution for Compositional Reasoning in Large Language Models
Feb 17, 2026Sarim ChaudhryCompositional Reasoning Test-Time Adaptation
Purdue University
PERSONA: Dynamic and Compositional Inference-Time Personality Control via Activation Vector Algebra
Feb 17, 2026Xiachong Feng, Liang Zhao, Weihong Zhong +5Controllable Text Generation Personality Modeling in Language Models
Harbin Institute of Technology · The University of Hong Kong
The Information Geometry of Softmax: Probing and Steering
Feb 17, 2026Kiho Park, Todd Nief, Yo Joong Choe +1Representation Geometry in Language Models Information Geometry
University of Chicago · INSEAD
Symmetry in language statistics shapes the geometry of model representations
Feb 16, 2026Dhruva Karkada, Daniel J. Korchinski, Andres Nava +2Representation Learning Neural Representation Geometry
1UC Berkeley · 2EPFL · 3Johns Hopkins +1
Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Experts
Feb 16, 2026Buze Zhang, Jinkai Tao, Zilang Zeng +4Parameter-Efficient Fine-Tuning Representation Geometry in Language Models
School of Software Engineering, Xi’an Jiaotong University, China · School of Information, Central University of Finance and Economics, Beijing, China · Department of Artificial Intelligence, Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China +2
StructLens: A Structural Lens for Language Models via Maximum Spanning Trees
Feb 10, 2026Haruki Sakajo, Frederikus Hudi, Yusuke Sakai +2LLM Interpretability Representation Geometry in Language Models
Nara Institute of Science and Technology (NAIST)
From Directions to Regions: Decomposing Activations in Language Models via Local Geometry
Feb 2, 2026Or Shafran, Shaked Ronen, Omri Fahn +3Language Model Steering LLM Interpretability
Blavatnik School of Computer Science and AI, Tel Aviv University, Israel · New York University, New York, NY, USA · Goodfire.
Language Steering for Multilingual In-Context Learning
Feb 2, 2026Neeraja Kirtane, Kuan-Hao HuangMultilingual Language Models Cross-Lingual Transfer
Texas A&M University
Functional Subspace, where language models can use vector algebra to solve problems
Feb 2, 2026Jung H. Lee, Sujith VijayanLLM Interpretability In-Context Learning
Pacific Northwest National Laboratory Seattle, WA · School of Neuroscience Virginia Tech Blacksburg, VA
From Associations to Activations: Comparing Behavioral and Hidden-State Semantic Geometry in LLMs
Jan 31, 2026Louis Schiekiera, Max Zimmer, Christophe Roux +2Representation Geometry in Language Models Computational Psycholinguistics
Computational Modelling Lab, Humboldt-Universität zu Berlin, Berlin, Germany · Department of Education and Psychology, Freie Universität Berlin, Berlin, Germany · Department for AI in Society, Science, and Technology, Zuse Institute Berlin, Germany +1
From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
Nov 27, 2025Florian Rottach, William Rudman, Bastian Rieck +2Representation Geometry in Language Models Text Embedding Evaluation
University of Tübingen · Boehringer Ingelheim GmbH, Biberach (Riss), Germany · The University of Texas at Austin +1
Contextual Representation Flow Across Depth in State-Space and Transformer Architectures
Oct 8, 2025Nhat M. Hoang, Do Xuan Long, Cong-Duy Nguyen +3State Space Models State Space Language Models
Nanyang Technological University, Singapore · National University of Singapore
Is This Just Fantasy? Language Model Representations Reflect Human Judgments of Event Plausibility
Jul 16, 2025Michael A. Lepori, Jennifer Hu, Ishita Dasgupta +3Representation Geometry in Language Models
Department of Computer Science, Brown University · Google DeepMind · Department of Cognitive & Psychological Sciences, Brown University
Localizing Persona Representations in LLMs
May 30, 2025Celia Cintas, Miriam Rateike, Erik Miehling +2LLM Interpretability Personality Modeling in Language Models
IBM Research Africa · IBM Research Europe

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A Gauge Theory of Superposition: Toward a Sheaf-Theoretic Atlas of Neural Representations

Hossein Javidnia

School of Computing, Dublin City University, Ireland

LLM Interpretability Representation Geometry in Language Models Neural Representation Geometry

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We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts. Contexts are clustered into a stratified context complex; each chart carries a local feature space and a local information-geometric metric (Fisher/Gauss-Newton) identifying predictively consequential feature interactions. This yields a Fisher-weighted interference energy and three measurable obstructions to global interpretability: (O1) local jamming (active load exceeds Fisher bandwidth), (O2) proxy shearing (mismatch between geometric transport and a fixed correspondence proxy), and (O3) nontrivial holonomy (path-dependent transport around loops). We prove and instantiate four results on a frozen open LLM (Llama-3.2-3B Instruct) using WikiText-103, a C4-derived English web-text subset, and the-stack-smol. (A) After constructive gauge fixing on a spanning tree, each chord residual equals the holonomy of its fundamental cycle, making holonomy computable and gauge-invariant. (B) Shearing lower-bounds a data-dependent transfer mismatch energy, turning

D_{\mathrm{shear}}

into an unavoidable failure bound. (C) We obtain non-vacuous certified jamming/interference bounds with high coverage and zero violations across seeds and hyperparameters. (D) Bootstrap and sample-size experiments show stable estimation of

D_{\mathrm{shear}}

and

D_{\mathrm{hol}}

, with improved concentration on well-conditioned subsystems.