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. 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
The continuous evolution of AI research pushes for more robust and complex models that can handle uncertainty and long-range dependencies, leading to innovations like fractional stochastic neural networks.
This development introduces new mathematical and computational tools for building more resilient and sophisticated AI, particularly in areas requiring uncertainty quantification, long memory, and robust performance.
The ability to model systems with fractional Brownian motion and quantify uncertainty more effectively could lead to more reliable AI applications in critical fields, improving their interpretability and trustworthiness.
- · AI researchers
- · High-reliability AI sectors
- · Financial modeling
- · Time series analysis
- · Traditional stochastic models
- · AI systems lacking uncertainty quantification
Improved performance and robustness of neural networks in tasks involving noisy data or long-term dependencies.
Accelerated development of AI agents capable of operating effectively in highly uncertain or volatile real-world environments.
Potential for new AI applications in scientific discovery and complex system control where current models fall short due to limitations in handling uncertainty and memory.
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Read at arXiv cs.LG