  We present a generalisation of Rosenblatt's traditional perceptron learning
algorithm to the class of proximal activation functions and demonstrate how
this generalisation can be interpreted as an incremental gradient method
applied to a novel energy function. This novel energy function is based on a
generalised Bregman distance, for which the gradient with respect to the
weights and biases does not require the differentiation of the activation
function. The interpretation as an energy minimisation algorithm paves the way
for many new algorithms, of which we explore a novel variant of the iterative
soft-thresholding algorithm for the learning of sparse perceptrons.
