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This work derives the edge of stability threshold from the directional Hessian and the gradient-alignment score with respect to the actual update taken by the optimizer, rather than the maximum curvature mode.
It has recently been found that deep learning often occurs at the"edge of stability (EoS),"where the maximum Hessian eigenvalue of the model is stabilized at a value reciprocal to the learning rate. However, what happens before we reach that regime? We fix a deep learning problem and vary first order optimization metho...
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