Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway
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Computer Science > Machine Learning
Title:Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway
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
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