MuProp: Unbiased Backpropagation for Stochastic Neural Networks

TL;DR

MuProp is an unbiased gradient estimator that enables effective training of stochastic neural networks with discrete variables, improving variance reduction and performance over previous methods.

Contribution

Introduces MuProp, a novel unbiased gradient estimator for stochastic networks that reduces variance using a control variate based on Taylor expansion.

Findings

MuProp achieves consistent performance across various tasks.

It provides an unbiased and well-behaved gradient estimate.

Outperforms prior estimators in structured output prediction.

Abstract

Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes it possible to learn very complex distributions. However, as backpropagation is not directly applicable to stochastic networks that include discrete sampling operations within their computational graph, training such networks remains difficult. We present MuProp, an unbiased gradient estimator for stochastic networks, designed to make this task easier. MuProp improves on the likelihood-ratio estimator by reducing its variance using a control variate based on the first-order Taylor expansion of a mean-field network. Crucially, unlike prior attempts at using backpropagation for training stochastic networks, the resulting estimator is unbiased and well behaved. Our experiments on structured output prediction and discrete latent variable modeling demonstrate that MuProp yields consistently good performance across a range of difficult tasks.