arXiv:2602. 14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms.
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv:2606. 30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory.
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv:2606. 06934v1 Announce Type: new Abstract: We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding.
arXiv:2607. 21716v1 Announce Type: new Abstract: Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics.
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
arXiv:2609.01034v1 Announce Type: new Abstract: The central flow of Cohen et al. (2025) is an empirically accurate continuous-time model of gradient descent at the edge of stability in deep learning,...
arXiv:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
arXiv:2604. 14669v2 Announce Type: replace Abstract: Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored.
arXiv:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.
The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.