arXiv:2608. 19762v1 Announce Type: cross Abstract: A minibatch can influence training beyond the update at which it is observed because AdamW stores past gradient information in its optimizer states.
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arXiv:2608.24593v1 Announce Type: new Abstract: Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether t...
arXiv:2608. 01997v1 Announce Type: new Abstract: Single-optimizer training is a poor fit for the distinct phases of deep network optimization: adaptive methods handle noisy early gradients well but overshoot flat minima, while SGD with momentum generalizes better in the late phase but converges slowly early on.
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv:2605. 29547v2 Announce Type: replace-cross Abstract: Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators.
The paper investigates the "edge of stability" phenomenon in deep learning, where Hessian eigenvalues remain stable above a classically predicted unstable threshold. It shows that many first‑order optimizers, including gradient descent, can violate this stability bound by up to a factor of 21.1, and that this deviation depends systematically on the optimizer used. The authors propose a new stability threshold based on the directional Hessian and gradient‑alignment score, which removes optimizer‑dependent offsets and offers consistent predictions while providing diagnostic tools to understand how optimizers balance temporal and spatial budgets.
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.