ARM: Augment-REINFORCE-Merge Gradient for Discrete Latent Variable Models
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To backpropagate the gradients through discrete stochastic layers, we encode the true gradients into a multiplication between random noises and the difference of the same function of two different sets of discrete latent variables, which are correlated with these random noises. The expectations of that multiplication over iterations are zeros combined with spikes from time to time. To modulate the frequencies, amplitudes, and signs of the spikes to capture the temporal evolution of the true gradients, we propose the augment-REINFORCE-merge (ARM) estimator that combines data augmentation, the score-function estimator, permutation of the indices of latent variables, and variance reduction for Monte Carlo integration using common random numbers. The ARM estimator provides low-variance and unbiased gradient estimates for the parameters of discrete distributions, leading to state-of-the-art performance in both auto-encoding variational Bayes and maximum likelihood inference, for discrete latent variable models with one or multiple discrete stochastic layers.
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