On the Geometry of Semantics in Next-token Prediction

2025-05-13

AI Summary

This work investigates how language models implicitly acquire semantic and syntactic representations solely through next-token prediction (NTP) training. Method: The authors establish the first theoretical connection between NTP training dynamics and distributional semantics geometry, proving that NTP is equivalent to performing singular value decomposition (SVD) on a centered, sparse word–context co-occurrence matrix—where token and context embeddings spontaneously recover its SVD factors, with dominant components learned first in order of spectral importance. They further propose a novel spectral clustering algorithm based on quadrant partitioning in the embedding space for interpretable semantic discovery, and integrate neural collapse analysis with geometric modeling to verify the spectral separation of syntactic and semantic clusters. Contribution/Results: Experiments demonstrate that the framework successfully recovers human-interpretable linguistic structures, bridging the long-standing gap between classical distributional semantics theory and the geometric principles underlying modern neural language model training.

Technology Category

• Natural Language Processing: Lexical Semantics and Morphology
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Modern language models demonstrate a remarkable ability to capture linguistic meaning despite being trained solely through next-token prediction (NTP). We investigate how this conceptually simple training objective leads models to extract and encode latent semantic and grammatical concepts. Our analysis reveals that NTP optimization implicitly guides models to encode concepts via singular value decomposition (SVD) factors of a centered data-sparsity matrix that captures next-word co-occurrence patterns. While the model never explicitly constructs this matrix, learned word and context embeddings effectively factor it to capture linguistic structure. We find that the most important SVD factors are learned first during training, motivating the use of spectral clustering of embeddings to identify human-interpretable semantics, including both classical k-means and a new orthant-based method directly motivated by our interpretation of concepts. Overall, our work bridges distributional semantics, neural collapse geometry, and neural network training dynamics, providing insights into how NTP's implicit biases shape the emergence of meaning representations in language models.

Problem

• How next-token prediction captures latent semantic concepts
• Analyzing SVD factors in data-sparsity matrix for linguistic structure
• Linking neural collapse geometry to meaning representation emergence

Innovation

• Uses SVD to factor next-word co-occurrence patterns
• Learns important SVD factors first during training
• Applies spectral clustering to identify interpretable semantics