AI RESEARCH
Why Adam Can Beat SGD: Second-Moment Normalization Yields Sharper Tails
arXiv CS.LG
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ArXi:2603.03099v2 Announce Type: replace Despite Adam nstrating faster empirical convergence than SGD in many applications, much of the existing theory yields guarantees essentially comparable to those of SGD, leaving the empirical performance gap insufficiently explained. In this paper, we uncover a key second-moment normalization in Adam and develop a stopping-time/martingale analysis that provably distinguishes Adam from SGD under the classical bounded variance model (a second moment assumption.