Eigenvalue Distributions for a Class of Covariance Matrices with Applications to Bienenstock-Cooper-Munro Neurons Under Noisy Conditions

TL;DR

This paper studies how noise correlations affect BCM neuron behavior by analyzing eigenvalue distributions of correlation matrices, revealing that high noise variance can prolong synaptic strength lifetimes, with implications for neural physiology.

Contribution

It introduces an analytical approach using the Wigner semicircular law to understand the impact of noise correlations on BCM neurons, combining theory with numerical validation.

Findings

High noise variance can extend synaptic lifetimes.

Correlations in input noise or lateral connections influence neuron dynamics.

Analytic eigenvalue distributions match numerical simulations.

Abstract

We analyze the effects of noise correlations in the input to, or among, BCM neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input LGN neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.