arXiv:2607. 29038v1 Announce Type: new Abstract: Fractional scientific machine learning requires numerical operators that can be differentiated, batched, accelerated, and composed with neural networks.
By Ning Hu, Haitao Duan, Shuqun Li, Chuyang Hu
arXiv:2510.05606v2 Announce Type: replace
Abstract: Fundamental limits to predictability are central to our understanding of many physical and computational systems. In deep learning, training outcom...
By Andrew Ly, Pulin Gong
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.
By Hwanseo Lee, Junseo Lee, Hyunju Kim
arXiv:2606. 08308v1 Announce Type: new Abstract: Predicting the generalization performance of deep neural networks without relying on hold-out validation data is a fundamental challenge in machine learning.
By Joao B. Florindo, Davi Wanderley Misturini
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.
The paper introduces the fractional Laplace neural operator (fLNO), a neural operator that embeds Volterra resolvent structures with non‑rational Laplace symbols into learned maps. It demonstrates that a single graph‑spectral layer can exactly represent the full linear Volterra solution for commuting excitation–Laplacian pairs, and establishes limits on the expressivity of finite rational realizations, showing they cannot capture non‑integer critical asymptotics. The authors also provide trainable parametrizations that enforce stability margins, a graphon‑transfer theorem, and empirical results on benchmark data, Chilean aftershock sequences, and renewal models, highlighting the fLNO’s ability to recover branching coordinates with few parameters while maintaining stability.
By Mauricio Herrera-Mar\'in