Deterministic Adam-Inspired Methods with Accelerated Convergence Rate

Excerpt

arXiv:2604.08742v2 Announce Type: replace-cross Abstract: Adam is widely used, but its convergence theory remains incomplete even in the deterministic full-batch setting because momentum and adaptive preconditioning are tightly coupled. For smooth convex objectives, we split the momentum variable through variable-and-operator splitting, which reveals the acceleration mechanism. We then combine a Hessian-driven correction with Adam-style feedback based on the gradient magnitude. The resulting Ada