# Fractional Stochastic Neural Networks

Source: [Fractional Stochastic Neural Networks](<https://www.sota2.com/research/paper/6a434d7cba73165dbb74394e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-01T05:00:12.177Z

Authors: Yuecai Han, Jianming Xu

Published: 2026-06-28T14:55:00.000Z

## Abstract

In this paper, we develop a fractional stochastic neural network with residual dynamics driven by fractional Brownian motion. By introducing a discrete stochastic maximum principle for the network, we construct the corresponding adjoint recursion. For deterministic network parameters, we prove mean square convergence of projected samplewise stochastic gradient descent. Numerical experiments include a closed form convergence test, noisy regression with uncertainty quantification, long memory time series generation and image classification under structured perturbations. The results identify settings in which fractional drivers improve long memory recovery or robustness relative to Brownian and deterministic baselines.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.29438>)

[PDF](<https://arxiv.org/pdf/2606.29438.pdf>)