Weber's law implies neural discharge more regular than a Poisson process

TL;DR

This paper demonstrates that neural spike trains obeying Weber's law are more regular than Poisson processes, especially in small populations or with shared weak correlations, linking psychophysical laws to neuronal firing properties.

Contribution

It establishes a quantitative connection between Weber's law and neural firing regularity, showing neurons exhibit less variability than Poisson processes under this law.

Findings

Single neuron spike train is less variable than Poisson process.

Weber's law holds in small populations or with shared weak correlations.

Regularity of neural firing supports Weber's law without population size restrictions.

Abstract

Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (< 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a Poisson process, Weber's law is true without any restriction on the population size. Biased competition attractor network also demonstrates that the coefficient of variation of interspike interval in the winning pool should be less than one for the validity of Weber's law. Our work links Weber's law with neural firing property quantitatively, shedding light on the relation between psychophysical behavior and neuronal responses.