Convergence analysis for differential equations modeling neural systems

Neural networks are often modeled by large systems of strongly coupled differential equations, where the number of equations corresponds to the number of neurons. Beyond their size, these differential systems also involve time delays, as the transmission of signals between neurons is not instantaneous. The time needed to compute numerical solutions for these systems can decrease significantly in parallel computing environments. In this talk, we introduce parallel numerical algorithms applied to neural networks and investigate their convergence properties. The number of processors that can be used in the computations may be any positive integer between 1 and N, where N represents the number of neurons in a given neural network. We derive error bounds for these algorithms and use them to conclude convergence properties. The theoretical results are illustrated by means of numerical examples in which solutions are computed in parallel computing environments.

Видео Convergence analysis for differential equations modeling neural systems канала CMMSE: Computational & Mathematics Methods