Paul Mineiro, Javier Movellan, Ruth Williams
We propose diffusion networks, a type of recurrent neural network with probabilistic dynamics, as models for learning natural signals that are continuous in time and space. We give a formula for the gradient of the log-likelihood of a path with respect to the drift parameters for a diffusion network. This gradient can be used to optimize diffusion networks in the nonequilibrium regime for a wide variety of problems paralleling techniques which have succeeded in engineering fields such as system identification, state estimation and signal filtering. An aspect of this work which is of particu(cid:173) lar interest to computational neuroscience and hardware design is that with a suitable choice of activation function, e.g., quasi-linear sigmoidal, the gradient formula is local in space and time.