Attention as Spacetime Curvature: A General Relativistic Analogy for Language Models

This article, "Attention as Spacetime Curvature: A General Relativistic Analogy for Language Models," proposes a novel conceptual framework for understanding Transformer architectures by drawing an analogy to Einstein's General Theory of Relativity. It posits that attention mechanisms in language models operate not merely as statistical computations but as a geometric phenomenon, where important tokens "curve" the information space, influencing the flow of meaning much like mass and energy curve spacetime, affecting the paths of objects and light. The paper introduces the core analogy by explaining how massive objects warp spacetime, causing other entities to follow curved "geodesic" paths. This concept is then directly applied to Transformer networks, where token importance is analogous to gravitational mass, and the propagation of information becomes akin to objects moving through a curved semantic space. Key aspects explored include: Attention as Gravitational Influence: The document argues that attention scores represent a "gravitational pull," determining how much one token affects another, with higher scores indicating stronger influence. The mathematical representation of Scaled Dot-Product Attention is likened to a potential field in gravity. Geodesics and Meaning Flow: The article suggests that token representations evolve by following geodesics, which are locally straight but globally curved paths, through an attention-curved representation space. This naturally explains contextual word meaning and disambiguation. Curvature and Representation Evolution: The concept of Riemannian curvature is introduced to measure how token representations diverge in this curved space, illustrating how attention patterns induce "curvature" that shapes information flow. Measurability and Applications: The paper proposes methods for quantifying this conceptual curvature using gradient-based and graph-theoretic analyses, such as Ollivier-Ricci curvature. It also discusses the practical applications of such analysis for model interpretability, optimization, and robustness. This Zenodo record contains the following components: Attention_As_Spacetime_Curvature_Latest_Version.pdf: The full text of the research article, detailing the proposed analogy between General Relativity and Transformer attention, including theoretical explanations, mathematical formulations, and discussions of potential applications. gravitational_deflection_simulator.py: Python script containing the gravitational light deflection simulator as discussed in Section 2 of the article. This script allows for visualization of spacetime curvature analogies. attention_bending_towards_tokens.py: Python script for visualizing attention's gravitational-like effects in Transformer models, identifying 'massive tokens' and their influence on information flow, as demonstrated in Section 2. These supplementary scripts are provided to ensure the reproducibility of the simulations and visualizations presented in the paper. Keywords: Attention Mechanisms, Transformers, General Relativity, Spacetime Curvature, Language Models, Information Geometry, Deep Learning, AI Interpretability, Natural Language Processing, Geodesics.