Disentangling Representation Evolution in Transformers through Directional Decomposition
Decomposes transformer representation updates into parallel and perpendicular components, linking geometry to editing robustness and better pretraining.
The paper decomposes learned transformer updates into parallel and perpendicular components relative to the hidden state, finding substantial parallel components beyond the residual identity path across pretrained models. Targeted edits reveal exclude-self value-space parallel manipulation is more robust than residual-space or perpendicular alternatives, and perpendicular error separates compression methods more clearly. Applying full-aggregate parallel suppression during from-scratch pretraining lowers validation loss and improves downstream averages, with the value-space variant strongest. Code is released on GitHub.
- Decomposes representation updates into parallel and perpendicular components
- Value-space exclude-self edits markedly more robust than alternatives
- Perpendicular error cleanly separates compression methods
- Parallel suppression during pretraining lowers validation loss; code released
Full article170 words · extracted from arxiv.org · click to collapse
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}.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.15975