Shared Global and Local Geometry of Language Model Embeddings

2025/03/27 by Andrew Lee, Lee, Andrew, Melanie Weber +5 · 3 voices · 16 citations
Computer Science · #Differential geometry #Dimension (graph theory) #Language model #Measure (data warehouse) #Natural Language Processing Techniques #Security token #Simple (philosophy) #Topology (electrical circuits)

paper · pdf · doi:10.48550/arxiv.2503.21073

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• The Geometry of Categorical and Hierarchical Concepts in Large Language Models
• The Platonic Representation Hypothesis
• Fishing for Magikarp: Automatically Detecting Under-trained Tokens in Large Language Models
• The Pile: An 800GB Dataset of Diverse Text for Language Modeling
• Adversarial Reprogramming of Neural Networks
• Deep Residual Learning for Image Recognition

Cited by

• Abstraction Induces the Brain Alignment of Language and Speech Models
• Better World Models Can Lead to Better Post-Training Performance
• From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
• Position: Require Frontier AI Labs To Release Small "Analog" Models
• Representation Potentials of Foundation Models for Multimodal Alignment: A Survey
• Transferring Linear Features Across Language Models With Model Stitching
• Jailbreak Transferability Emerges from Shared Representations
• Training-Free Tokenizer Transplantation via Orthogonal Matching Pursuit
• Do different prompting methods yield a common task representation in language models?
• Signal in the Noise: Polysemantic Interference Transfers and Predicts Cross-Model Influence
• Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Control
• Density-Aware Noise Mechanisms for Differential Privacy on Riemannian Manifolds via Conformal Transformation
• Disentangling MLP Neuron Weights in Vocabulary Space
• Characterizing Human Semantic Navigation in Concept Production as Trajectories in Embedding Space
• Differential syntactic and semantic encoding in LLMs
• The Geometry of Self-Verification in a Task-Specific Reasoning Model

Discussions

• Next time a reviewer asks, “Why didn’t you include [insert newest LM]?”, depending on your claims you could argue that your findings will generalize to other models, based on our work! Paper link: arx [bsky, 21 points, 1 comments]
• Congrats to the best poster awardees! @ajyl.bsky.social Shared Geometry of LMs: arxiv.org/pdf/2503.21073 Antonia Karamolegkou, Multimodal LMs for Visual Impairment: aclanthology.org/2025.acl-lon... @g [bsky, 7 points, 1 comments]
• Breakthrough research reveals something stunning: AI models from different companies are secretly converging toward the same internal "mental maps" of language. Despite being trained separately, they' [bsky, 1 points, 1 comments]

Related

• Measuring Intrinsic Dimension of Token Embeddings
• The Origins of Representation Manifolds in Large Language Models
• Mapping Semantic & Syntactic Relationships with Geometric Rotation
• The Geometry of Tokens in Internal Representations of Large Language Models
• Token embeddings violate the manifold hypothesis