Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality

TL;DR

This paper investigates how various information measures of spike trains depend on time resolution, revealing structural properties and universality classes of neuron models, and demonstrating their utility in understanding neural coding mechanisms.

Contribution

It introduces a detailed analysis of information measures for spike trains, showing their dependence on time resolution and identifying universal properties across neuron models.

Findings

Time-resolution dependence reveals interspike interval correlations.

Excess entropy and statistical complexity are universal in continuous-time limit.

Different neuron types can be distinguished based on information measure behaviors.

Abstract

The mutual information between stimulus and spike-train response is commonly used to monitor neural coding efficiency, but neuronal computation broadly conceived requires more refined and targeted information measures of input-output joint processes. A first step towards that larger goal is to develop information measures for individual output processes, including information generation (entropy rate), stored information (statistical complexity), predictable information (excess entropy), and active information accumulation (bound information rate). We calculate these for spike trains generated by a variety of noise-driven integrate-and-fire neurons as a function of time resolution and for alternating renewal processes. We show that their time-resolution dependence reveals coarse-grained structural properties of interspike interval statistics; e.g., $\tau$-entropy rates that diverge less quickly than the firing rate indicate interspike interval correlations. We also find evidence that the excess entropy and regularized statistical complexity of different types of integrate-and-fire neurons are universal in the continuous-time limit in the sense that they do not depend on mechanism details. This suggests a surprising simplicity in the spike trains generated by these model neurons. Interestingly, neurons with gamma-distributed ISIs and neurons whose spike trains are alternating renewal processes do not fall into the same universality class. These results lead to two conclusions. First, the dependence of information measures on time resolution reveals mechanistic details about spike train generation. Second, information measures can be used as model selection tools for analyzing spike train processes.