Next talk
Date: Tuesday, April 1st 2025 (15:30-16:30, room A709)
Speaker: (Université Côte d'Azur)
Title: Kalikow decomposition for the study of neuronal networks: simulation and learning
Abstract: Kalikow decomposition is a decomposition of stochastic processes (usually finite state discrete time processes but also more recently point processes) that consists in picking at random a finite neighborhood in the past and then make a transition in a Markov manner. This kind of approach has been used for many years to prove existence of some processes, especially their stationary distribution. In particular, it allows to prove the existence of processes that model infinite neuronal networks, such as Hawkes like processes or Galvès-Löcherbach processes. But beyond mere existence, this decomposition is a wonderful tool to simulate such network, as an open physical system, that from a computational point of view could be competitive with the most performant brain simulations. This decomposition is also a source of inspiration to understand how local rules at each neuron can make the whole network learn.
Figure: Simulation of neuron 0 activity by Kalikow decomposition. Neuron 0 is immersed in an infinite Z² complete graph with Gaussian weights. In a) number of requests and time spent on the other neurons to simulate neuron 0 for 50 s. On the right, zoom on the repartitions of the requests in time for the 8 neurons surrounding 0.