[2606.05219] Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway
[Submitted on 29 May 2026]
Title:Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway
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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-driven symmetry breaking predicted by GF, oscillations at the Edge of Stability subsequently override this tendency and drive the network into a re-balancing phase, where signals redistribute across pathways. Together, these results clarify how depth shapes pathway competition and explain why large-step GD favors shared representations rather than persistent single-pathway dominance.
Comments: ICML 2026
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2606.05219 [cs.LG]
(or arXiv:2606.05219v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.05219
arXiv-issued DOI via DataCite
Submission history
From: Hee-Sung Kim [view email] [v1] Fri, 29 May 2026 13:32:18 UTC (1,000 KB)
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