arXiv:2607. 15505v1 Announce Type: cross Abstract: Fractional gradient descent (FGD) incorporates long-range memory through Caputo-type operators and has been shown to improve stability in ill-conditioned and nonconvex optimization problems.
arXiv:2511. 13592v2 Announce Type: replace-cross Abstract: The existing method of GS-PowerOpt solves the non-convex optimization problem of the form $\max_{\boldsymbol{x} \in \mathbb{R}^d} f(\boldsymbol{x})$ through maximizing a Gaussian-smoothed surrogate $F_{N,\sigma}(\boldsymbol{\mu}) = \mathbb{E}_{\boldsymbol{x}\sim\mathcal{N}(\boldsymbol{\mu},\sigma^2 I_d)}[e^{N f(\boldsymbol{x})}]$.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2106. 06998v5 Announce Type: replace Abstract: Training convolutional neural networks at scale demands substantial memory, largely because intermediate activations must be stored for backpropagation.
arXiv:2608. 06912v1 Announce Type: new Abstract: The top-$k$ operation is a fundamental building block of modern sparse computation, enabling token routing, expert activation, memory selection, and attention pruning.
arXiv:2608. 12879v1 Announce Type: new Abstract: Fractional partial differential equations describe nonlocal dynamics, but discovering them from noisy data is difficult because fractional differentiation amplifies high-frequency measurement noise and the derivative orders are unknown.
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
Spiking Neural Networks (SNNs) are well-regarded for their biological plausibility and energy efficiency in processing sequential data. However, dominant SNN architectures typically rely on first-order Ordinary Differential Equations (ODEs) to govern neuronal state transitions.
arXiv:2608. 12009v1 Announce Type: cross Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness.
arXiv:2608. 14636v1 Announce Type: cross Abstract: Fractional optimization methods and fractal activation functions are two independent directions for improving neural network training.
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:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
arXiv:2607. 16261v1 Announce Type: cross Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments.