A mathematical approach on memory capacity of a simple synapses model

Pascal Helson (1)

1 TOSCA - TO Simulate and CAlibrate stochastic models

Network models of Memory: Capacity of neural networks in memorising external inputs is a complex problem which has given rise to numerous research. It is widely accepted that memory sits where communication between two neurons takes place, in synapses. It involves a huge number of chemical reactions, cascades, ion flows, protein states and even more mechanisms, which makes it really complex. Such a complexity stresses the need of simplifying models: this is done in network models of memory. Problem: Most of these models don't take into account both synaptic plasticity and neural dynamic. Adding dynamics on the weights makes the analysis more difficult which explains that most models consider either a neural or a synaptic weight dynamic. We decided to study the binary synapses model of Amit and Fusi (1994), model we wish to complete with a neural network afterwards in order to get closer to biology. Purpose: Propose a rigorous mathematical approach of the model of Amit and Fusi (1994) as part of a more ambitious aim which is to have a general mathematical framework adapted to many models of memory.

Domaines: Probabilités [math.PR]; Sciences cognitives

Pascal Helson. A mathematical approach on memory capacity of a simple synapses model. International Conference on Mathematical NeuroScience (ICMNS), Jun 2018, Antibes, France. ⟨hal-01957292⟩