Adam-HNAG is a splitting-based reformulation of Adam that yields the first convergence proof for Adam-type methods, including accelerated rates, in convex smooth optimization.
arXiv preprint arXiv:1808.05671 , year=
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Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
Muon-MVR2 attains the optimal anytime convergence rate of ~O(T^{-1/3}) in stochastic non-convex settings under horizon-free schedules.
Proposes federated adaptive optimizers (FedAdagrad, FedAdam, FedYogi) with convergence analysis for non-convex objectives under data heterogeneity and reports empirical gains over FedAvg.
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
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