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: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.
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:2510. 03164v2 Announce Type: replace Abstract: Learning rate warm-up -- increasing the learning rate at the beginning of training -- has become a ubiquitous heuristic in modern deep learning, yet its theoretical foundations remain poorly understood.
We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion equation as typical representatives. The work employs a geometry-adapted integration split featuring a spatially dependent near-field radius, which decomposes the fractional Laplacian into three contributions: a singular near field, a regular interior far field, and an analytical exterior far field.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.
arXiv:2606. 27140v1 Announce Type: new Abstract: We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion equation as typical representatives.