Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway

arXiv:2606.05219v1 Announce Type: new Abstract: Recent analyses of multi-pathway Deep Linear Networks use Gradient Flow to predict a "winner-takes-all" specialization in which path symmetry breaks and each feature concentrates in a single pathway. In this work, we show that discrete Gradient Descent (GD) with a large step size tells a different story. We prove that single-path solutions are sharp minima, whereas distributing signals across pathways reduces sharpness by a factor that decreases with both the number of pathways and depth. Consequently, while early training reproduces the depth-dr

Source: arXiv cs.LG — read the full report at the original publisher.

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