Influence of discrete synaptic signals on the dynamics of balanced neural networks

Abstract

In 2024, the Nobel Prize in Physics was awarded for work that laid the foundation for the development of machine learning based on artificial neural networks. This event can be considered a public recognition of the role of mathematical models like the Hopfield model and the use of the mathematical apparatus of statistical physics and quantum mechanics to describe collective dynamics
in them. Despite the fact that neuronal network dynamics is mediated by discrete synaptic signals,
the theoretical description of the endogenous noise in such networks is constructed within the framework of the diffusion approximation. This approach has a significant drawback, since in fact a discrete set of signals is represented as continuous Gaussian noise. It turns out that the result of this approach is the actual “blindness” of the obtained equations to some regimes of collective dynamics of the system: in particular, to the possibility of hysteresis transitions between asynchronous and oscillatory dynamics in a balanced neural network with a sparse net of connections. The paper describes a recently introduced full mean-field formalism that takes into account the effective synaptic shot noise in a sparse network of spiking neurons. Two mechanisms of global oscillations in the system depending on the degree of network sparsity are also found and explained. The developed formalism was tested on two models of neuron dynamics: quadratic integrate-and-fire neurons and the Morris–Lecar model