Constraints on Hebbian and STDP learned weights of a spiking neuron

TL;DR

This paper provides a mathematical analysis of how Hebbian and STDP learning rules constrain synaptic weights in spiking neurons with normalization, offering insights into convergence and applications like novelty detection.

Contribution

It derives explicit relations between normalized weights and promotion/demotion probabilities for Hebbian and STDP rules, aiding in understanding convergence and practical applications.

Findings

Normalized weights approximate promotion probabilities in Hebbian learning.

In STDP, normalized weights reflect the difference between promotion and demotion probabilities.

Relations help verify convergence and enable novelty detection, demonstrated on MNIST.

Abstract

We analyse mathematically the constraints on weights resulting from Hebbian and STDP learning rules applied to a spiking neuron with weight normalisation. In the case of pure Hebbian learning, we find that the normalised weights equal the promotion probabilities of weights up to correction terms that depend on the learning rate and are usually small. A similar relation can be derived for STDP algorithms, where the normalised weight values reflect a difference between the promotion and demotion probabilities of the weight. These relations are practically useful in that they allow checking for convergence of Hebbian and STDP algorithms. Another application is novelty detection. We demonstrate this using the MNIST dataset.