Constraints on Hebbian and STDP learned weights of a spiking neuron
This work provides practical mathematical relations for researchers and practitioners working with Hebbian and STDP learning rules to check algorithm convergence and apply novelty detection.
This paper mathematically analyzes the constraints on weights learned by Hebbian and STDP rules in spiking neurons with weight normalization. It finds that normalized Hebbian weights approximate promotion probabilities, while STDP weights reflect the difference between promotion and demotion probabilities, enabling convergence checks and novelty detection, demonstrated on MNIST.
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.