Statistical physics of neural systems with non-additive dendritic coupling

TL;DR

This paper uses statistical physics to analyze how nonlinear dendritic processing in neurons influences single neuron responses and enhances associative memory robustness in neural networks, revealing an optimal number of dendrites for memory function.

Contribution

It introduces a novel statistical physics framework to study the effects of nonlinear dendritic summation on neural computation and memory performance.

Findings

Nonlinear dendrites improve network convergence.

Dendritic nonlinearities enhance memory robustness against noise.

An optimal number of dendrites maximizes memory performance.

Abstract

How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such non-additive dendritic processing on single neuron responses and the performance of associative memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality.