Disentangling Representation Evolution in Transformers through Directional Decomposition

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arxiv:2609.15975

Published on Sep 14

· Submitted by

Shwai He on Sep 16

· ByteDance

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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 https://github.com/Shwai-He/Transformer-Geometry{project repository}.

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shwai-he

Paper submitter 7 days ago

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edited 7 days ago

❓ Core Question: Are direction-preserving updates in Transformers merely redundant rescaling? We find that the answer depends strongly on where the geometry is defined. 🔍 What We Did & Found: We decompose learned transformations into components parallel and perpendicular to the current representation, across both residual space and attention value space. • Parallel components are widespread beyond the residual identity path, yet their functional role is highly space-dependent. • In value space, preserving the direct self-message while suppressing the non-self parallel component is markedly more robust than residual-space or perpendicular interventions. 🚀 Practical Applications:

1. Model Compression 📉: Perpendicular error more clearly distinguishes pruning- and quantization-induced distortions.

2. From-Scratch Pretraining ⚡: Full-aggregate parallel suppression lowers validation-loss trajectories and improves downstream task averages, with the value-space variant being the strongest. 🌐 Interactive Project Page & Studio: https://shwai-he.github.io/Transformer-Geometry/ 📜 arXiv Paper: https://arxiv.org/abs/2609.15975 💻 Code & Artifacts: https://github.com/Shwai-He/Transformer-Geometry

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