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arXiv Machine Learning By Xiaoyang Li, Runni Zhou

Singular Curvature in ReLU Training:Differentiation and the Gradient-Flow Limit Need Not Commute

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The paper investigates the relationship between discrete gradient descent (GD) and its continuous-time gradient-flow counterpart in the context of ReLU neural networks. It shows that while GD states converge over a finite horizon, the exact discrete derivatives obtained via automatic differentiation do not necessarily match the derivative of the limiting flow, due to singular curvature at activation events. The authors provide a Stieltjes representation that separates continuous regional Hessians from atomic interface curvature, revealing rank-one discrepancies at activation jumps and demonstrating that even globally strongly convex residual-ReLU losses can exhibit large sensitivity ratios on certain initialization sets.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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