Does a larger neural network mean greater information transmission efficiency?

TL;DR

This paper investigates how increasing the size of neural networks affects information transmission efficiency, finding that larger networks converge slowly to a saturation point, implying limited efficiency gains but increased reliability.

Contribution

It provides a theoretical and numerical analysis of mutual information in large neural networks using Shannon's theory and Levy-Baxter models, revealing slow convergence to saturation.

Findings

Mutual information converges slowly to a saturation level as network size increases.

Increasing neurons enhances reliability but not transmission efficiency significantly.

Analysis combines theoretical and numerical approaches with Levy-Baxter neural models.

Abstract

Realistic modeling of brain involves large number of neurons. The important question is how this size affects transmission efficiency? Here, these issue is studied in terms of Shannon's Theory. Mutual Information between input and output signals for simple class of networks with an increasing number of neurons is analyzed theoretically and numerically. Levy-Baxter neural model is applied. It turned out, that for these networks the Mutual Information converges, with increasing size, asymptotically very slowly to saturation level. This suggests that from certain level, the increase of neurons number does not imply significant increase in transmission efficiency, contributes rather to reliability.