Author

Xiao-Yang Li

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Preprint Aug 2026

Branch Geometry and Finite-Radius Sensitivity of Hard-ReLU Training

This work characterize the intervening regime in which the perturbation radius is proportional to the GD step, and identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

Xiao-Yang Li, Run-Ni Zhou, Xin Yan · 0 citations

#machine learning Preprint Aug 2026

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

Gradient descent (GD) is explicit Euler for gradient flow, but a state-accurate continuous-time surrogate need not remain accurate after differentiation. At every fixed nonresonant step size, ordinary automatic differentiation exactly differentiates the executed hard-ReLU GD program. We prove that, over a fixed finite...

Xiao-Yang Li, Run-Ni Zhou · 0 citations