Mean-field Models of Neural Networks with Generic Heterogeneous Connections
Time: 2024-09-10
Published By: He Liu
Speaker(s): Datong Zhou (Laboratoire J.-L. Lions , Sorbonne Université)
Time: 16:00-17:00 September 12, 2024
Venue: Room 29, Quan Zhai, BICMR
We investigate the mean-field limits of large-scale networks of interacting biological neurons, represented by the so-called integrate-and-fire models. However, we do not assume any prior structure on the network but consider instead any connection weights that obey certain types of mean-field scaling. When the networks are dense, we are able to achieve a limit that resembles the widely recognized form of mean-field limit, through a graphon limit that tracks the role of individual neurons in the network. When the networks are potentially sparse, mathematically interpreting the role of individual neurons becomes increasingly difficult. Instead, we introduce novel statistical notions that directly describe the large-scale dynamics of networks. These are joint works with P.-E. Jabin and V. Schmutz.
