Disentangling Representation Evolution in Transformers through Directional Decomposition

2026-09-14

AI Summary

研究通过方向分解分析Transformer表示的演变，揭示了平行和垂直分量的作用，并展示了其在编辑鲁棒性、压缩诊断及训练干预中的应用。

Abstract

Transformer representations evolve through learned additive transformations that either preserve their current direction or redirect it. We study this evolution as a functional geometry, decomposing learned updates into parallel and perpendicular components. Across pretrained models, we find substantial parallel components beyond the residual identity path. We then apply the decomposition in two spaces: to attention and MLP updates relative to the hidden state, and to attention value aggregation relative to the current token's value. Targeted edits reveal a strongly space-dependent asymmetry: exclude-self value-space parallel manipulation is markedly more robust than residual-space and perpendicular counterparts, preserving the direct self message while scaling only the non-self aggregate. The same decomposition gives a component-resolved description of compression-induced update error: perpendicular error separates compression methods more clearly than parallel error. Extensive experiments further demonstrate that full-aggregate parallel suppression during from-scratch pretraining lowers validation-loss trajectories and improves downstream averages, with the value-space variant strongest. Together, these results connect representation geometry to editing robustness, compression diagnosis, and training-time intervention. Code is available in the \href{https://github.com/Shwai-He/Transformer-Geometry}{project repository}.

Problem

• Transformer
• representation evolution
• directional decomposition
• robustness
• compression

Innovation

• directional decomposition
• parallel and perpendicular components
• representation evolution
• compression-induced update error
• training-time intervention