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. 29038v1 Announce Type: new Abstract: Fractional scientific machine learning requires numerical operators that can be differentiated, batched, accelerated, and composed with neural networks.
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...
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: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.
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.
arXiv:2606. 29438v1 Announce Type: cross Abstract: In this paper, we develop a fractional stochastic neural network with residual dynamics driven by fractional Brownian motion.
arXiv:2206. 04359v3 Announce Type: replace Abstract: One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data.
arXiv:2603. 06861v2 Announce Type: replace Abstract: Activation functions are fundamental to deep neural networks, governing gradient flow, optimization stability, and representational capacity.
arXiv:2510. 22450v3 Announce Type: replace-cross Abstract: The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons.
arXiv:2609.36314v1 Announce Type: new Abstract: State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for...
arXiv:2403.04545v4 Announce Type: replace Abstract: Scaling factors in residual branches have emerged as a prevalent method for boosting neural network performance, especially in normalization-free a...