Clustering of neural codewords revealed by a first-order phase transition

TL;DR

This study uncovers a complex, clustered organization of neural codewords in retinal data, revealing a phase transition that influences how neural information is represented and processed.

Contribution

It demonstrates that neural codewords form distinct clusters separated by entropy gaps, similar to associative memory networks, and highlights the special role of the all-silent state.

Findings

Neural codewords are divided into multiple clusters with entropy gaps.

The codeword structure resembles that of associative memory networks.

The all-silent state is densely surrounded and centrally located in the codeword space.

Abstract

A network of neurons in the central nervous system collectively represents information by its spiking activity states. Typically observed states, i.e., codewords, occupy only a limited portion of the state space due to constraints imposed by network interactions. Geometrical organization of codewords in the state space, critical for neural information processing, is poorly understood due to its high dimensionality. Here, we explore the organization of neural codewords using retinal data by computing the entropy of codewords as a function of Hamming distance from a particular reference codeword. Specifically, we report that the retinal codewords in the state space are divided into multiple distinct clusters separated by entropy-gaps, and that this structure is shared with well-known associative memory networks in a recallable phase. Our analysis also elucidates a special nature of the all-silent state. The all-silent state is surrounded by the densest cluster of codewords and located within a reachable distance from most codewords. This codeword-space structure quantitatively predicts typical deviation of a state-trajectory from its initial state. Altogether, our findings reveal a non-trivial heterogeneous structure of the codeword-space that shapes information representation in a biological network.