Adam or Gauss-Newton? A Comparative Study In Terms of Basis Alignment and SGD Noise

Title:Adam or Gauss-Newton? A Comparative Study In Terms of Basis Alignment and SGD Noise

Abstract:Preconditioned methods are central to deep learning optimization. Predominant approaches include computationally light diagonal preconditioners such as Adam, which rely on gradient statistics, and second-order methods such as Gauss-Newton (GN), which capture richer curvature information. Seeking the best of both worlds, we disentangle the preconditioner design space into several factors, separating the choice of diagonal scaling (Adam-style versus GN-style) from 1) the basis choices under which the diagonal scaling operates, and 2) the gradient noises from mini-batching. Our theoretical results show that GN's optimality for linear regression no longer holds under a poorly chosen basis under both population and stochastic updates, or a move from linear regression to a non-convex variant of logistic regression. In these settings, Adam-style methods offer genuine advantages over curvature-inspired preconditioning, rather than serving merely as a tractable proxy. Empirical results on synthetic problems and CIFAR-10 support these findings.

Machine Learning (cs.LG)

arXiv:2510.13680 [cs.LG]

(or arXiv:2510.13680v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2510.13680 Focus to learn more arXiv-issued DOI via DataCite

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