Stochastic Neural Networks with Monotonic Activation Functions


Siamak Ravanbakhsh, Barnabas Poczos, Jeff Schneider, Dale Schuurmans, Russell Greiner ;
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:809-818, 2016.


We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences. This family, that we call exponential family RBM (Exp-RBM), is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearity for each neuron. Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBM can learn useful representations using novel stochastic units.

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