Energy-efficient population coding constrains network size of a neuronal array system

TL;DR

This paper mathematically demonstrates that neuronal arrays have an optimal size balancing energy efficiency and reliable information transmission, which varies with noise levels and signal thresholds.

Contribution

It provides a general mathematical solution showing the existence of an optimal neuronal number that minimizes energy cost while maintaining reliable coding in noisy environments.

Findings

Optimal neuronal number minimizes energy cost per neuron.

Optimal size decreases with noise for subthreshold signals.

Optimal size increases with noise for suprathreshold signals.

Abstract

Here, we consider the open issue of how the energy efficiency of neural information transmission process in a general neuronal array constrains the network size, and how well this network size ensures the neural information being transmitted reliably in a noisy environment. By direct mathematical analysis, we have obtained general solutions proving that there exists an optimal neuronal number in the network with which the average coding energy cost (defined as energy consumption divided by mutual information) per neuron passes through a global minimum for both subthreshold and superthreshold signals. Varying with increases in background noise intensity, the optimal neuronal number decreases for subthreshold and increases for suprathreshold signals. The existence of an optimal neuronal number in an array network reveals a general rule for population coding stating that the neuronal number should be large enough to ensure reliable information transmission robust to the noisy environment but small enough to minimize energy cost.