Logarithmic distributions prove that intrinsic learning is Hebbian

TL;DR

This paper shows that neural spike rates, synaptic weights, and intrinsic excitability follow lognormal distributions across various brain regions, and demonstrates that Hebbian learning rules are essential for maintaining these distributions.

Contribution

The study provides evidence that intrinsic excitability and synaptic weights are governed by Hebbian plasticity, explaining the origin of lognormal distributions in neural properties.

Findings

Lognormal distributions are consistent across multiple brain areas.

Hebbian learning is necessary for maintaining lognormal distributions.

Intrinsic gains and weights are shaped by similar plasticity rules.

Abstract

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.