AI RESEARCH
Non-Euclidean Gradient Descent Operates at the Edge of Stability
arXiv CS.LG
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ArXi:2603.05002v2 Announce Type: replace The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian approaches and then hovers near the stability threshold $2/\eta$ during gradient descent (GD) with step size $\eta$. Despite (apparently) violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We provide an interpretation of EoS through the lens of Directional Smoothness [Mishkin, 2024.