arXiv:2505. 01423v2 Announce Type: replace-cross Abstract: Efficient computation of min-max problems is a central question in optimization, learning, games, and control.
arXiv:2606. 01764v1 Announce Type: cross Abstract: We revisit the convergence guarantees of the Extragradient (EG) method for unconstrained biaffine min-max optimization.
arXiv:2608. 10418v1 Announce Type: cross Abstract: Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications.
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
The paper derives an exact discrete‑time law that captures how learning‑rate schedules and weight decay interact in scale‑invariant neural networks, showing that a single scalar quantity governs the effective step size. It demonstrates that the balance point between contraction and expansion is intrinsically unstable, leading to recurrent dynamics when using constant learning rates with weight decay. The authors extend this analysis to various optimizers and datasets, confirming the law’s precision and showing that performance peaks sharply at the predicted boundary.
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
HyCO is a hybrid neural solver that combines a sequential reinforcement learning (RL) solver with a global diffusion model (DM) to tackle combinatorial optimization problems. The RL component builds an initial solution prefix, after which HyCO switches to a conditional DM to finish the remaining decisions. The authors provide a theoretical framework showing that this hybrid approach yields lower expected regret than either method alone, identify an optimal trigger step for the switch, and implement a lightweight adaptive trigger based on policy entropy and RL‑DM disagreement, achieving consistent performance gains across benchmarks.
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:2607. 22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity.
arXiv:2606. 05888v1 Announce Type: new Abstract: Retry-based objectives such as pass@K and max@K optimize the best return obtained from multiple sampled trajectories, and recent work has shown that they can promote exploration without explicit exploration bonuses.
arXiv:2610.01546v1 Announce Type: cross Abstract: Primal-dual hybrid gradient (PDHG) methods solve large-scale linear programs (LPs) using GPU-friendly matrix-vector products and projections, but the...
The paper investigates how normalization makes neural networks scale‑invariant, creating a feedback loop between learning‑rate schedules and weight decay that controls the effective step size of the optimizer. It derives an exact discrete‑time law showing that a single scalar quantity captures all schedule and decay effects, with norm growth providing a self‑quenching counter‑force that defines a sharp boundary between contraction‑ and expansion‑dominated regimes. Through exact analysis of a normalized regression model and experiments on MLPs, CNNs, GPT‑2, and various datasets, the authors demonstrate that constant learning rates with weight decay are intrinsically unstable, leading to recurrent dynamics, and that adaptive optimizers exhibit weaker stabilization under normalization. "whyItMatters":"The study provides a precise, actionable rule for controlling training dynamics and schedule design in modern deep learning by isolating a single governing quantity for scale‑invariant optimization."
The paper introduces ZFO, a lightweight framework that separates direction selection from step-size determination in large‑scale neural network optimization. ZFO uses a trusted first‑order optimizer to pick a search direction and then performs only two additional objective evaluations to build a local curvature‑aware model, selecting an adaptive step within a bounded interval. The authors provide theoretical guarantees for reliable curvature estimation, near‑optimal step selection, and convergence to a stationary point, and demonstrate that ZFO improves optimization and final performance over fixed‑step first‑order baselines on language‑model fine‑tuning tasks.