arXiv AI By Valeria Ruscio, Keiran Thompson

The Geometry of Learning: Read-Write Asymmetry Across Training

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The paper investigates how pretraining and alignment stages of transformer training affect weight updates in different matrix groups. By examining the residual stream’s shared coordinate system, it finds that alignment updates to query and key matrices align with the principal input subspace, whereas updates to output matrices remain largely random relative to the prediction subspace. This pattern persists across objectives and training stages, indicating that the geometry of updates is determined by the training phase rather than the specific objective.

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