Gaussian Process Neurons

We propose a method to learn stochastic activation functions for use in probabilistic neural networks. First, we develop a framework to embed stochastic activation functions based on Gaussian processes in probabilistic neural networks. Second, we analytically derive expressions for the propagation of means and covariances in such a network, thus allowing for an efficient implementation and training without the need for sampling. Third, we show how to apply variational Bayesian inference to regularize and efficiently train this model. The resulting model can deal with uncertain inputs and implicitly provides an estimate of the confidence of its predictions. Like a conventional neural network it can scale to datasets of arbitrary size and be extended with convolutional and recurrent connections, if desired.