На 01.07.2024 г. от 14:00 ч. в стая 578 на ИМИ и онлайн в Zoom
ще се състои поредната сбирка на семинара по
Диференциални уравнения и математическа физика.
Доклад на тема
p-Adic Numbers, Neural Networks, Deep Learning, and Statistical Field Theories
ще изнесе Prof. W. A. Zuniga-Galindo from University of Texas Rio Grande Valley.
АБСТРАКТ
The talk aims to glimpse our recent research work on the mathematical foundations of hierarchical neural networks. I plan to cover the following topics: (1) the non-Archimedean Wilson-Cowan Model; (2) p-adic Cellular Neural Networks; (3) p-Adic Statistical Field Theory and Deep Boltzmann Machines. In the first part of the talk, I present a hierarchical version of the Wilson-Cowan model, one of the most relevant models in theoretical neuroscience (see Reference [1]). The second part is dedicated to p-adic cellular neural networks and their applications to image processing (see Reference [2]). Finally, I plan to present the results of Reference [3] on the connections between deep Boltzmann machines and Euclidean quantum field theories.
In deep learning architectures, the neurons are organized in layers to form a hierarchical structure. These systems comprise several subsystems and are characterized by emergent behavior resulting from nonlinear interactions between subsystems for multiple levels of organization. The non-Archimedean analysis is the natural tool for constructing mathematical models of hierarchically organized systems.
РЕФЕРЕНЦИИ
[1] W.A. Zúñiga-Galindo, B.A. Zambrano-Luna. Hierarchical Wilson-Cowan Models and Connection Matrices. Entropy (Basel). 2023 Jun 16;25(6):949. https://doi.org/10.3390/
[2] B. A. Zambrano-Luna, W.A. Zúñiga-Galindo, p-adic cellular neural networks: Applications to image processing, Physica D: Nonlinear Phenomena, Volume 446, 2023, 133668. https://doi.org/10.1016/j.
[3] W. A. Zúñiga-Galindo, C He, B A Zambrano-Luna, p-Adic statistical field theory and convolutional deep Boltzmann machines, Progress of Theoretical and Experimental Physics, Volume 2023, Issue 6, June 2023, 063A01, https://doi.org/10.1093/ptep/
ZOOM линк:
https://us02web.zoom.us/j/