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.

Latest papers

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

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
Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
May 1, 2026Sheridan Feucht, Tal Haklay, Usha Bhalla +9Numerical Reasoning in Language Models LLM Interpretability
aNortheastern University · bTechnion IIT · cHarvard University +1
Escaping Mode Collapse in LLM Generation via Geometric Regulation
May 1, 2026Xin Du, Kumiko Tanaka-IshiiLanguage Model Steering Decoder-Only Language Models
Department of Communications and Computer Engineering, Waseda University, Tokyo, Japan · Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, China · Department of Computer Science and Engineering, Waseda University, Tokyo, Japan
Representational Curvature Modulates Behavioral Uncertainty in Large Language Models
Apr 27, 2026Jack King, Evelina Fedorenko, Eghbal A. HosseiniNeural Representation Geometry Autoregressive Language Modeling
Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 · Google DeepMind
Convergent Evolution: How Different Language Models Learn Similar Number Representations
Apr 22, 2026Deqing Fu, Tianyi Zhou, Mikhail Belkin +2Fourier Feature Embeddings Frequency-Domain Feature Learning
University of Southern California · UC San Diego
Cell-Based Representation of Relational Binding in Language Models
Apr 21, 2026Qin Dai, Benjamin Heinzerling, Kentaro InuiLLM Interpretability Representation Probing
1Tohoku University · 2RIKEN AIP · 3MBZUAI
Exploring Concreteness Through a Figurative Lens
Apr 20, 2026Saptarshi Ghosh, Tianyu JiangFigurative Language Understanding LLM Interpretability
University of Cincinnati
Predict and Reconstruct: Joint Objectives for Self-Supervised Language Representation Learning
Apr 16, 2026Aimen BoukhariJoint-Embedding Predictive Architecture Masked Language Modeling
´Ecole Nationale Sup´erieure d’Informatique (ESI), Algiers , Algeria
Geometric Routing Enables Causal Expert Control in Mixture of Experts
Apr 15, 2026Ivan Ternovtsii, Yurii BilakMixture-of-Experts Interpretability Mixture-of-Experts Expert Specialization
Department of Software Systems, Uzhhorod National University, Narodna sq. 3, Uzhhorod, Ukraine, 88000 · HengeBytes
Rhetorical Questions in LLM Representations: A Linear Probing Study
Apr 15, 2026Louie Hong Yao, Vishesh Anand, Yuan Zhuang +1Pragmatic Reasoning in Language Models Representation Geometry in Language Models
Independent Researcher · University of Cincinnati · Amazon
Linear Probe Accuracy Scales with Model Size and Benefits from Multi-Layer Ensembling
Apr 15, 2026Erik Nordby, Tasha Pais, Aviel ParrackLanguage Model Probing Deception in Language Models
Georgia Institute of Technology, Atlanta, Georgia, USA · Independent Researcher · Stanford University, Stanford, California, USA
H-Probes: Extracting Hierarchical Structures From Latent Representations of Language Models
Apr 15, 2026Cutter Dawes, Aryan Sharma, Angelos Ioannis Lagos +1Representation Geometry in Language Models Hierarchical Representation Learning
Supervised Program for Alignment Research · Yale University · Harvard University
Towards Platonic Representation for Table Reasoning: A Foundation for Permutation-Invariant Retrieval
Apr 13, 2026Willy Carlos Tchuitcheu, Tan Lu, Ann DoomsTable Reasoning Tabular Representation Learning
Department of Mathematics and Data Science, Vrije Universiteit Brussel (VUB), Brussels, Belgium · Data Science Lab, Royal Library of Belgium (KBR), Brussels, Belgium
Identity as Attractor: Geometric Evidence for Persistent Agent Architecture in LLM Activation Space
Apr 13, 2026Vladimir VasilenkoRepresentation Geometry in Language Models Cognitive Architectures for AI Agents
Independent Researcher, Rapallo, Italy
The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts
Apr 13, 2026Thomas Walker, Ahmed Imtiaz Humayun, Randall Balestriero +1Neural Network Interpretability Mechanistic Interpretability
Rice University · Google Research · Brown University
Shared Emotion Geometry Across Small Language Models: A Cross-Architecture Study of Representation, Behavior, and Methodological Confounds
Apr 13, 2026Jihoon JeongRepresentation Geometry in Language Models Emotion Representation in Language Models
Department of Electrical Engineering and Computer Science, Daegu Gyeongbuk Institute of Science and Technology (DGIST) · ModuLabs
Do BERT Embeddings Encode Narrative Dimensions? A Token-Level Probing Analysis of Time, Space, Causality, and Character in Fiction
Apr 12, 2026Beicheng Bei, Hannah Hyesun Chun, Chen Guo +1Language Model Probing Representation Geometry in Language Models
Department of Linguistics, University of Rochester, 503 Lattimore Hall, Rochester, NY 14627
The Myth of Expert Specialization in MoEs: Why Routing Reflects Geometry, Not Necessarily Domain Expertise
Apr 10, 2026Xi Wang, Soufiane Hayou, Eric NalisnickMixture-of-Experts Expert Specialization Mixture of Experts
Johns Hopkins University
On the Representational Limits of Quantum-Inspired 1024-D Document Embeddings: An Experimental Evaluation Framework
Apr 10, 2026Dario MaioQuantum-Inspired ML Text Embedding Evaluation
Department of Computer Science and Engineering, University of Bologna, Italy
Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics
Apr 9, 2026Raphael Bernas, Fanny Jourdan, Antonin Poché +1Representation Geometry in Language Models LLM Training
MICS, CentraleSupelec, Université Paris-Saclay · IRT Saint Exupéry, Toulouse, France · Mila - Quebec AI Institute, Montreal, Canada +1
Linear Representations of Hierarchical Concepts in Language Models
Apr 9, 2026Masaki Sakata, Benjamin Heinzerling, Takumi Ito +2Hierarchical Representation Learning LLM Interpretability
Tohoku University · RIKEN · Langsmith Inc. +2
Learning is Forgetting: LLM Training As Lossy Compression
Apr 8, 2026Henry C. Conklin, Tom Hosking, Tan Yi-Chern +5Language Model Pretraining LLM Compression
Princeton University · Cohere

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

Sibayan Mitra, Dhruv Kumar

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

Neural Representation Geometry Representation Geometry in Language Models

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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.