Natural-gradient learning for spiking neurons

TL;DR

This paper proposes a natural gradient-based learning rule for spiking neurons, addressing parametrization issues in synaptic plasticity and explaining several biological phenomena through a Riemannian geometry framework.

Contribution

It introduces a novel synaptic learning rule based on natural gradient descent for spiking neurons, linking mathematical optimization with biological plasticity mechanisms.

Findings

Derives a biologically plausible synaptic learning rule.

Explains dendritic democracy and heterosynaptic plasticity.

Suggests evolution may have used natural gradient principles.

Abstract

In many normative theories of synaptic plasticity, weight updates implicitly depend on the chosen parametrization of the weights. This problem relates, for example, to neuronal morphology: synapses which are functionally equivalent in terms of their impact on somatic firing can differ substantially in spine size due to their different positions along the dendritic tree. Classical theories based on Euclidean gradient descent can easily lead to inconsistencies due to such parametrization dependence. The issues are solved in the framework of Riemannian geometry, in which we propose that plasticity instead follows natural gradient descent. Under this hypothesis, we derive a synaptic learning rule for spiking neurons that couples functional efficiency with the explanation of several well-documented biological phenomena such as dendritic democracy, multiplicative scaling and heterosynaptic plasticity. We therefore suggest that in its search for functional synaptic plasticity, evolution might have come up with its own version of natural gradient descent.