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PreprintarXiv licencearXiv

A samplewise backpropagation method for neural networks driven by fractional Brownian motion

  • Yuecai Han
  • Jianming Xu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{han2026samplewise,
  title = {{A samplewise backpropagation method for neural networks driven by fractional Brownian motion}},
  author = {Yuecai Han and Jianming Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.29438},
  eprint = {2606.29438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29438},
}
RIS
TY  - UNPB
TI  - A samplewise backpropagation method for neural networks driven by fractional Brownian motion
AU  - Yuecai Han
AU  - Jianming Xu
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.29438
UR  - https://arxiv.org/abs/2606.29438
AB  - 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.
ER  -