Fractional stochastic search algorithms: modelling complex systems via AI
- The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {๐ต๐ป๐ก,๐กโฅ0} with the Hurst parameter ๐ปโ(0,1). We define and discuss the properties of fractional stochastic processes, {๐ต๐ป๐ก,๐กโฅ0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.
| Author of HS Reutlingen | Herzog, Bodo |
|---|---|
| URN: | urn:nbn:de:bsz:rt2-opus4-46131 |
| DOI: | https://doi.org/10.3390/math11092061 |
| Erschienen in: | Mathematics |
| Publisher: | MDPI |
| Place of publication: | Basel |
| Document Type: | Journal article |
| Language: | English |
| Publication year: | 2023 |
| Volume: | 11 |
| Issue: | 9 |
| Page Number: | 11 |
| First Page: | 1 |
| Last Page: | 11 |
| Article Number: | 2061 |
| DDC classes: | 510 Mathematik |
| Open access?: | Ja |
| Licence (German): |  ย ย Creative Commons - CC BY - Namensnennung 4.0 International |
