mlsanityData to 14 Oct 2026

Shared Global and Local Geometry of Language Model Embeddings

arXiv 2503.21073 ↗First posted 27 Mar 2025cs.CL cs.LGcited by 36

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Abstract (arXiv)

Researchers have recently suggested that models share common representations. In our work, we find numerous geometric similarities across the token embeddings of large language models. First, we find ``global'' similarities: token embeddings often share similar relative orientations. Next, we characterize local geometry in two ways: (1) by using Locally Linear Embeddings, and (2) by defining a simple measure for the intrinsic dimension of each embedding. Both characterizations allow us to find local similarities across token embeddings. Additionally, our intrinsic dimension demonstrates that embeddings lie on a lower dimensional manifold, and that tokens with lower intrinsic dimensions often have semantically coherent clusters, while those with higher intrinsic dimensions do not. Based on our findings, we introduce EMB2EMB, a simple application to linearly transform steering vectors from one language model to another, despite the two models having different dimensions.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Builds on 42 of its 52 references that are in the map. First posted on arXiv 27 Mar 2025.

Builds on

42 of 52 references.

References · 42

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2024The Llama 3 Herd of Modelscited by 14,715
  3. 2013Distributed Representations of Words and Phrases and their Compositionalitycited by 3,474
  4. 2020The Pile: An 800GB Dataset of Diverse Text for Language Modelingcited by 2,411
  5. 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,998
  6. 2023Inference-Time Intervention: Eliciting Truthful Answers from a Language Modelcited by 1,302
  7. 2020RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Modelscited by 1,255
  8. 2023Steering Llama 2 via Contrastive Activation Additioncited by 1,085
  9. 2016ConceptNet 5.5: An Open Multilingual Graph of General Knowledgecited by 1,067
  10. 2022Discovering Language Model Behaviors with Model-Written Evaluationscited by 836
  11. 2020Prevalence of Neural Collapse during the terminal phase of deep learning trainingcited by 719
  12. 2023The Linear Representation Hypothesis and the Geometry of Large Language Modelscited by 716
30 more
  1. 2022GPT-NeoX-20B: An Open-Source Autoregressive Language Modelcited by 713
  2. 2024OLMo: Accelerating the Science of Language Modelscited by 613
  3. 2022Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Spacecited by 532
  4. 2024Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Researchcited by 483
  5. 2024The Platonic Representation Hypothesiscited by 382
  6. 2023Emergent Linear Representations in World Models of Self-Supervised Sequence Modelscited by 319
  7. 2014Understanding image representations by measuring their equivariance and equivalencecited by 243
  8. 2021Contrastive Learning Inverts the Data Generating Processcited by 221
  9. 2021Revisiting Model Stitching to Compare Neural Representationscited by 209
  10. 2013Exploiting Similarities among Languages for Machine Translationcited by 191
  11. 2024A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicitycited by 185
  12. 2019Emerging Cross-lingual Structure in Pretrained Language Modelscited by 181
  13. 2024The Geometry of Categorical and Hierarchical Concepts in Large Language Modelscited by 159
  14. 2023A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operationscited by 144
  15. 2022Linearly Mapping from Image to Text Spacecited by 142
  16. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 122
  17. 2018Adversarial Reprogramming of Neural Networkscited by 116
  18. 2023The geometry of hidden representations of large transformer modelscited by 112
  19. 2023Circuit Component Reuse Across Tasks in Transformer Language Modelscited by 108
  20. 2024Universal Neurons in GPT2 Language Modelscited by 102
  21. 2017Residual Connections Encourage Iterative Inferencecited by 77
  22. 2024Fishing for Magikarp: Automatically Detecting Under-trained Tokens in Large Language Modelscited by 46
  23. 2019Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiplescited by 38
  24. 2024Linguistic Collapse: Neural Collapse in (Large) Language Modelscited by 38
  25. 2018Factors Influencing the Surprising Instability of Word Embeddingscited by 33
  26. 2024Implicit Geometry of Next-token Prediction: From Language Sparsity Patterns to Model Representationscited by 24
  27. 2025Activation Space Interventions Can Be Transferred Between Large Language Modelscited by 19
  28. 2024Algorithmic Capabilities of Random Transformerscited by 17
  29. 2024The representation landscape of few-shot learning and fine-tuning in large language modelscited by 15
  30. 2020Analyzing the Surprising Variability in Word Embedding Stability Across Languagescited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 11; 2026: 25.

36 papers.

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  1. 2025Transferring Linear Features Across Language Models With Model Stitchingcited by 21
  2. 2025Token embeddings violate the manifold hypothesiscited by 16
  3. 2026Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Controlcited by 16
  4. 2025The Geometry of Self-Verification in a Task-Specific Reasoning Modelcited by 13
  5. 2025Do different prompting methods yield a common task representation in language models?cited by 11
  6. 2025Representation Potentials of Foundation Models for Multimodal Alignment: A Surveycited by 11
  7. 2026From Data Statistics to Feature Geometry: How Correlations Shape Superpositioncited by 10
  8. 2026Differential syntactic and semantic encoding in LLMscited by 7
  9. 2026Learning Through Noise: Why Subliminal Learning Works and When It Failscited by 7
  10. 2025Jailbreak Transferability Emerges from Shared Representationscited by 6
  11. 2025From Topology to Retrieval: Decoding Embedding Spaces with Unified Signaturescited by 5
  12. 2025Signal in the Noise: Polysemantic Interference Transfers and Predicts Cross-Model Influencecited by 4
24 more
  1. 2025Training-Free Tokenizer Transplantation via Orthogonal Matching Pursuitcited by 4
  2. 2025Better World Models Can Lead to Better Post-Training Performancecited by 4
  3. 2026GeoSteer: Faithful Chain-of-Thought Steering via Latent Manifold Gradientscited by 4
  4. 2026Zipage: Maintain High Request Concurrency for LLM Reasoning through Compressed PagedAttentioncited by 4
  5. 2026The Indra Representation Hypothesis for Multimodal Alignmentcited by 4
  6. 2026Latent Structure of Affective Representations in Large Language Modelscited by 4
  7. 2026Disentangling MLP Neuron Weights in Vocabulary Spacecited by 3
  8. 2025Position: Require Frontier AI Labs To Release Small "Analog" Modelscited by 2
  9. 2026Abstraction Induces the Brain Alignment of Language and Speech Modelscited by 2
  10. 2026Characterizing Human Semantic Navigation in Concept Production as Trajectories in Embedding Spacecited by 2
  11. 2026Scale Determines Whether Language Models Organize Representation Geometry for Predictioncited by 2
  12. 2026Decoding in Geometry: Alleviating Embedding-Space Crowding for Complex Reasoningcited by 1
  13. 2026What Cosine Similarity of Label Representations Can and Cannot Tell uscited by 1
  14. 2026Tensor Product Representation Probes Reveal Shared Structure Across Linear Directionscited by 1
  15. 2026DreamReader: An Interpretability Toolkit for Text-to-Image Modelscited by 0
  16. 2026The Cost of Language: Centroid Erasure Exposes and Exploits Modal Competition in Multimodal Language Modelscited by 0
  17. 2026RDP LoRA: Geometry-Driven Identification for Parameter-Efficient Adaptation in Large Language Modelscited by 0
  18. 2026Coordinates of Capability: A Unified MTMM-Geometric Framework for LLM Evaluationcited by 0
  19. 2026Your CLIP has 164 dimensions of noise: Exploring the embeddings covariance eigenspectrum of contrastively pretrained vision-language transformerscited by 0
  20. 2026Structure Retention in Embedding Spaces as a Predictor of Benchmark Performancecited by 0
  21. 2026Some Tokens Behave like Magnets: Revealing Linguistic Organization in the Layers of Language Modelscited by 0
  22. 2026Quantifying Behavioral Tails in Black-Box Language Modelscited by 0
  23. 2026Scale, Drivers, and Limits of Representational Alignment Across Large Language Modelscited by 0
  24. 2026Geometric Structure Predicts Per-Example Neighborhood Loss Under PCA Truncationcited by 0

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  1. 2025Bridging the Dimensional Chasm: Uncover Layer-wise Dimensional Reduction in Transformers through Token Correlation
  2. 2026RiLM: Parameter-Efficient Language Modeling via Geodesic Decoding
  3. 2025The Origins of Representation Manifolds in Large Language Models
  4. 2025How Language Directions Align with Token Geometry in Multilingual LLMs
  5. 2026Cross-Architecture Steering Transfer in Language Models: A Systematic Empirical Study
  6. 2026A Geometric Perspective on Next-Token Prediction in Large Language Models: Three Emerging Phases
  7. 2026Symmetry in language statistics shapes the geometry of model representations
  8. 2026Learning Representations through Token Prediction: Geometry, Approximation, and Downstream Guarantees