# Bayesian Spiking Neural Networks

Published:

Implementation of the paper Homeostatic plasticity in Bayesian spiking networks as Expectation Maximization with posterior constraints by Habenschuss et al. This paper gives learning rules for a spiking neural network just based on Bayesian reasoning; therefore, the method can be used for unsupervised training of networks.

Contains code to runs different experiments on the proposed model and also on a model that is based not on a Binomial but Gaussian input distribution.

The code was written and the experiments conducted during a one week lasting seminar at the Max-Planck Institute for Dynamics and Self-Organization in 2019.

## Key insights

• eta_b has to be sufficiently large, otherwise homeostasis is not strong enough to keep r similar for all output neurons
• Even though the paper claims that a factor of 10 between the learning rates is sufficient, we find out that A_k(V) contributes exponentially while b_k contributes only linearly. Therefore, a factor of ten between eta_V and eta_b is not always optimal.
• Too few neurons for causes lead to learning of superposition states
• Network can reconstruct images is was not trained on

When images of digits between zero and five with the same ratio are shown to a network with 12 output neurons, for each class two neurons that are class-receptive arise. The neurons slowly learn to react to one of the input types.