arXiv:2603.03099v2 Announce Type: replace-cross
Abstract: Despite Adam demonstrating 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). In particular, we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a $delta^-1/2$ dependence on the confidence parameter $delta$, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a $delta^-1$ dependence.
Dissociable contributions of cortical thickness and surface area to cognitive ageing: evidence from multiple longitudinal cohorts.
Cortical volume, a widely-used marker of brain ageing, is the product of two genetically and developmentally dissociable morphometric features: thickness and area. However, it remains




