Adam under Generalized Smoothness with Second-Moment-Type Stochastic Gradients

Excerpt

arXiv:2609.37787v2 Announce Type: replace Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framework, however, existing analyses rely on strong tail assumptions on the stochastic gradients, such as almost-sure boundedness or sub-Gaussianity. Whether Adam converges on generalized smooth objectives under only second moment information on the stochastic gradients, without such concentration ass