The Curved Spacetime of Transformer Architectures

• URL: http://arxiv.org/abs/2511.03060v1
• Date: Tue, 04 Nov 2025 22:58:40 GMT
• Title: The Curved Spacetime of Transformer Architectures
• Authors: Riccardo Di Sipio, Jairo Diaz-Rodriguez, Luis Serrano,
• Abstract summary: We present a geometric framework for understanding Transformer-based language models, drawing an explicit analogy to General Relativity.<n>We show that token embeddings should not traverse straight paths in feature space; instead, their layer-wise steps should bend and reorient as interactions mediated by embedding space curvature.
• Score: 0.3670422696827525
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a geometric framework for understanding Transformer-based language models, drawing an explicit analogy to General Relativity. Queries and keys induce an effective metric on representation space, and attention acts as a discrete connection that implements parallel transport of value vectors across tokens. Stacked layers provide discrete time-slices through which token representations evolve on this curved manifold, while backpropagation plays the role of a least-action principle that shapes loss-minimizing trajectories in parameter space. If this analogy is correct, token embeddings should not traverse straight paths in feature space; instead, their layer-wise steps should bend and reorient as interactions mediated by embedding space curvature. To test this prediction, we design experiments that expose both the presence and the consequences of curvature: (i) we visualize a curvature landscape for a full paragraph, revealing how local turning angles vary across tokens and layers; (ii) we show through simulations that excess counts of sharp/flat angles and longer length-to-chord ratios are not explainable by dimensionality or chance; and (iii) inspired by Einstein's eclipse experiment, we probe deflection under controlled context edits, demonstrating measurable, meaning-consistent bends in embedding trajectories that confirm attention-induced curvature.

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