# Natural-gradient learning for spiking neurons

arXiv: https://arxiv.org/abs/2011.11710 · HTML: https://mlsanity.com/paper/2011.11710/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Bayesian Continual Learning via Spiking Neural Networks](https://mlsanity.com/paper/2208.13723/) (2022)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [Covariant spatio-temporal receptive fields for spiking neural networks](https://mlsanity.com/paper/2405.00318/) (2024)
- [Spike-based alignment learning solves the weight transport problem](https://mlsanity.com/paper/2503.02642/) (2025)

## Abstract (arXiv)

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.