Representation Geometry in Language Models

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Overview

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.

Latest papers

CardsList

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

  1. Geometric Properties of the Voronoi Tessellation in Latent Semantic Manifolds of Large Language Models

    Apr 8, 2026Marshall BrettRepresentation Geometry in Language ModelsInformation Geometry

    MARS Labs

  2. When Safety Geometry Collapses: Fine-Tuning Vulnerabilities in Agentic Guard Models

    Apr 8, 2026Ismail Hossain, Sai Puppala, Jannatul Ferdaus +4LLM GuardrailsLLM Safety Alignment

    Department of Computer Science, University of Texas at El Paso, TX, USA 79902 · School of Computing, Southern Illinois University Carbondale, IL, USA 62901 · Hanyang University, Seoul, South Korea +1

  3. Latent Structure of Affective Representations in Large Language Models

    Apr 8, 2026Benjamin J. Choi, Melanie WeberEmotion Representation in Language ModelsRepresentation Geometry in Language Models

    Harvard University

  4. The Illusion of Superposition? A Principled Analysis of Latent Thinking in Language Models

    Apr 7, 2026Michael Rizvi-Martel, Guillaume Rabusseau, Marius MosbachContinuous Latent ReasoningLLM Interpretability

    Mila – Quebec AI Institute · Universit´e de Montr´eal · McGill University

  5. Toward Consistent World Models with Multi-Token Prediction and Latent Semantic Enhancement

    Apr 7, 2026Qimin Zhong, Hao Liao, Haiming Qin +4Multi-Token PredictionLatent World Models

    Shenzhen University · Microsoft Research Asia

  6. LAG-XAI: A Lie-Inspired Affine Geometric Framework for Interpretable Paraphrasing in Transformer Latent Spaces

    Apr 7, 2026Olexander Mazurets, Olexander Barmak, Leonid Bedratyuk +1Transformer InterpretabilityRepresentation Geometry in Language Models

    Department of Computer Science, Khmelnytskyi National University, Khmelnytskyi, 29016, Ukraine · Department of Theoretical Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, 03187, Ukraine · Laboratory of Communicative Information Technologies, V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv, 03187, Ukraine

  7. LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals

    Apr 7, 2026Lihao Sun, Hang Dong, Bo Qiao +3LLM ReasoningRepresentation Geometry in Language Models

    Microsoft

  8. Turbulence-like 5/3 spectral scaling in contextual representations of language as a complex system

    Apr 7, 2026Zhongxin Yang, Chun Bao, Yuanwei Bin +2Representation Geometry in Language Models

    College of Engineering, Peking University, Beijing, 100871, China · Shenzhen Tenfong Technology Co., Ltd., Shenzhen 518000, China · Mechanical Engineering, Pennsylvania State University, State College, PA, 16802, USA

  9. On the Geometry of Positional Encodings in Transformers

    Apr 6, 2026Giansalvo CirrincioneMultidimensional ScalingPositional Encoding

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

  10. Multilingual Language Models Encode Script Over Linguistic Structure

    Apr 6, 2026Aastha A K Verma, Anwoy Chatterjee, Mehak Gupta +1Multilingual Language ModelsCross-Lingual Representation Alignment

    Indian Institute of Technology Delhi, New Delhi, India · Indian Institute of Technology Delhi, Abu Dhabi, UAE

  11. Under Pressure: Emotional Framing Induces Measurable Behavioral Shifts and Structured Internal Geometry in Small Language Models

    Apr 6, 2026Rana Muhammad UsmanFraming Effects in Language ModelsEmotion Representation in Language Models

    Independent Researcher

  12. Hallucination Basins: A Dynamic Framework for Understanding and Controlling LLM Hallucinations

    Apr 6, 2026Kalyan Cherukuri, Lav R. VarshneyHallucination in Language ModelsLLM Hallucination Mitigation

    Illinois Mathematics and Science Academy, Illinois, USA · AI Innovation Institute, Stony Brook University, New York, USA

  13. Same Geometry, Opposite Noise: Transformer Magnitude Representations Lack Scalar Variability

    Apr 6, 2026Jon-Paul CacioliRepresentation Geometry in Language Models

    Independent Researcher, Melbourne, Australia

  14. On the Invariants of Softmax Attention

    Apr 6, 2026Wonsuk LeeSoftmax AttentionAttention Head Analysis

    Seoul National University & SK Hynix America

  15. Measuring Representation Robustness in Large Language Models for Geometry

    Apr 3, 2026Vedant Jawandhia, Yash Sinha, Murari Mandal +2LLM EvaluationRepresentation Geometry in Language Models

    Department of Computer Science and Information Systems, BITS Pilani · School of Computer Science, KIIT University · Department of Mathematics, BITS Pilani

  16. The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason

    Apr 3, 2026Yi LiuRepresentation Geometry in Language Models

  17. Finding Belief Geometries with Sparse Autoencoders

    Apr 3, 2026Matthew LevinsonRepresentation Geometry in Language ModelsTransformer Interpretability

    Independent Researcher

  18. On the Geometric Structure of Layer Updates in Deep Language Models

    Apr 2, 2026Jun-Sik YooRepresentation Geometry in Language ModelsLLM Interpretability

    Institute of Basic Science, Korea University, 145 Anam-ro, Seoul, South Korea 02841.

  19. Grounded Token Initialization for New Vocabulary in LMs for Generative Recommendation

    Apr 2, 2026Daiwei Chen, Zhoutong Fu, Chengming Jiang +12Language Model Vocabulary ExpansionLarge Language Model-Based Recommendation

    University of Wisconsin-Madison · LinkedIn Corporation · Northeastern University +1

  20. In-context superposition: human-like working memory interference in large language models

    Apr 1, 2026Hua-Dong Xiong, Li Ji-An, Jiaqi Huang +3Working Memory in Language ModelsLLM Interpretability

    School of Psychological and Brain Sciences, Georgia Tech · Department of Psychology, New York University · Department of Cognitive Science, Indiana University Bloomington +3

  21. What Cosine Similarity of Label Representations Can and Cannot Tell us

    Mar 31, 2026Beatrix M. G. Nielsen, Andreas GrivasRepresentation Geometry in Language Models

    IT University of Copenhagen · School of Mathematics, University of Edinburgh

  22. Categorical Perception in Large Language Model Hidden States: Structural Warping at Digit-Count Boundaries

    Mar 30, 2026Jon-Paul CacioliTokenization in Language ModelsRepresentation Geometry in Language Models

    Independent Researcher, Melbourne, Australia

  23. Weight Tying Biases Token Embeddings Towards the Output Space

    Mar 27, 2026Antonio Lopardo, Avyukth Harish, Catherine Arnett +1Language ModelingRepresentation Geometry in Language Models

    EleutherAI · University of California Berkeley

  24. How Pruning Reshapes Features: Sparse Autoencoder Analysis of Weight-Pruned Language Models

    Mar 26, 2026Hector Borobia, Elies Seguí-Mas, Guillermina Tormo-CarbóLLM PruningRepresentation Geometry in Language Models

    VRAIN – Valencian Research Institute for Artificial Intelligence, Universitat Politècnica de València, Valencia, Spain · Department of Economics and Social Sciences, Universitat Politècnica de València, Valencia, Spain · Department of Business Organisation, Universitat Politècnica de València, Valencia, Spain

  25. A visual observation on the geometry of UMAP projections of the difference vectors of antonym and synonym word pair embeddings

    Mar 25, 2026Rami LuistoRepresentation Geometry in Language ModelsWord Embeddings

    Faculty of Information Technology, University of Jyväskylä, Jyväskylä; HUS Helsinki University Hospital, Helsinki; Digital Workforce Services, Helsinki.

  26. Steering Code LLMs with Activation Directions for Language and Library Control

    Mar 24, 2026Md Mahbubur Rahman, Arjun Guha, Harshitha MenonLanguage Model SteeringCode Language Models

    Iowa State University · Northeastern University · Lawrence Livermore National Laboratory

  27. The Geometric Price of Discrete Logic: Context-driven Manifold Dynamics of Number Representations

    Mar 24, 2026Long Zhang, Dai-jun Lin, Wei-neng ChenRepresentation Geometry in Language ModelsLLM Interpretability

    School of Computer Science and Engineering, South China University of Technology, Guangzhou City, Guangdong Province, China

  28. Improving LLM Final Representations with Inter-Layer Geometry

    Mar 24, 2026Tom Ulanovski, Eyal Blyachman, Maya Bechler-SpeicherGraph Neural NetworksRepresentation Geometry in Language Models

    Blavatnik School of Computer Science, Tel Aviv University · Tel Aviv University · Meta AI

  29. Riding Brainwaves in LLM Space: Understanding Activation Patterns Using Individual Neural Signatures

    Mar 23, 2026Ajan Subramanian, Sumukh Bettadapura, Rohan SathishEEG DecodingLanguage Model Probing

  30. Pooling and Semantic Shift: The Fundamental Challenges in Long Text Embedding and Retrieval

    Mar 22, 2026Hang Gao, Wujiang Xu, Kai Mei +1Text EmbeddingsText Embedding Models

    Rutgers University