Natural-gradient learning for spiking neurons.

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Machine Learning Theory

Background:

• Normative theories of synaptic plasticity often exhibit parametrization dependence, where weight updates are influenced by the chosen representation of weights.
• This dependence is exemplified by neuronal morphology, where functionally similar synapses can vary in size based on their dendritic location, leading to inconsistencies in Euclidean-gradient descent models.
• Classical synaptic plasticity models struggle to reconcile functional equivalence with anatomical variations.

Purpose of the Study:

• To address the parametrization dependence in synaptic plasticity theories.
• To propose a novel framework for synaptic plasticity based on Riemannian geometry and natural-gradient descent.
• To derive a synaptic learning rule that explains key biological phenomena.

Main Methods:

• Application of Riemannian geometry to model synaptic plasticity.
• Derivation of a natural-gradient descent-based synaptic learning rule for spiking neurons.
• Theoretical analysis linking the proposed rule to biological observations.

Main Results:

• A synaptic learning rule derived from natural-gradient descent in Riemannian geometry resolves parametrization dependence.
• The proposed rule successfully explains several biological phenomena, including dendritic democracy, multiplicative scaling, and heterosynaptic plasticity.
• The framework demonstrates how functional efficiency can be coupled with biologically observed plasticity mechanisms.

Conclusions:

• Natural-gradient descent within a Riemannian geometric framework provides a robust solution to parametrization-dependent synaptic plasticity.
• This approach offers a unified explanation for diverse biological synaptic plasticity phenomena.
• Evolution may have favored natural-gradient descent principles for optimizing synaptic plasticity in neural systems.