  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.
