Learning as filtering: implications for spike-based plasticity

TL;DR

This paper introduces the Synaptic Filter, a filtering-based learning rule for spiking neural networks that incorporates uncertainty and improves performance and generalization over traditional gradient methods.

Contribution

It derives a novel filtering-based learning rule for spiking networks, linking it to biological plasticity and demonstrating its computational advantages.

Findings

Filtering improves weight estimation accuracy.

Filtering outperforms gradient rules under model mismatch.

Synaptic Filter aligns with and predicts STDP dynamics.

Abstract

Most normative models in computational neuroscience describe the task of learning as the optimisation of a cost function with respect to a set of parameters. However, learning as optimisation fails to account for a time varying environment during the learning process; and the resulting point estimate in parameter space does not account for uncertainty. Here, we frame learning as filtering, i.e., a principled method for including time and parameter uncertainty. We derive the filtering-based learning rule for a spiking neuronal network - the Synaptic Filter - and show its computational and biological relevance. For the computational relevance, we show that filtering in combination with Bayesian regression improves performance compared to a gradient learning rule with optimal learning rate in terms of weight estimation. Furthermore, the filtering-based rule outperforms gradient-based rules in the presence of model mismatch, indicating a better generalisation performance. The dynamics of the mean of the Synaptic Filter is consistent with the spike-timing dependent plasticity (STDP) while the dynamics of the variance makes novel predictions regarding spike-timing dependent changes of EPSP variability. Moreover, the Synaptic Filter explains experimentally observed negative correlations between homo- and heterosynaptic plasticity.