Low Bias Low Variance Gradient Estimates for Hierarchical Boolean Stochastic Networks

Jul 12, 2020



Stochastic neural networks with discrete random variables are an important class of models for their expressiveness and interpretability. Since direct differentiation and backpropagation is not possible, Monte Carlo gradient estimation techniques are a popular alternative. Efficient stochastic gradient estimators, such Straight-Through and Gumbel-Softmax, work well for shallow stochastic models. Their performance, however, suffers with hierarchical, more complex models. We focus on hierarchical stochastic networks with multiple layers of Boolean latent variables. To analyze such networks, we introduce the framework of harmonic analysis for Boolean functions to derive an analytic formulation for the bias and variance in the Straight-Through estimator. Exploiting these formulations, we propose FouST, a low-bias and low-variance gradient estimation algorithm that is just as efficient. Extensive experiments show that FouST performs favorably compared to state-of-the-art biased estimators and is much faster than unbiased ones.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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