Reintroducing Straight-Through Estimators as Principled Methods for Stochastic Binary Networks

TL;DR

This paper systematically analyzes straight-through estimators for stochastic binary networks, providing a principled foundation, clarifying their properties, and enhancing their theoretical understanding for training binary neural networks.

Contribution

It offers a complete derivation and analysis of ST estimators within the SBN model, explaining their properties, limitations, and connections to optimization methods like mirror descent.

Findings

ST estimators are valid as estimators in SBN models.

Existing empirical ST methods can be justified theoretically.

The analysis reveals how latent weights emerge from optimization processes.

Abstract

Training neural networks with binary weights and activations is a challenging problem due to the lack of gradients and difficulty of optimization over discrete weights. Many successful experimental results have been achieved with empirical straight-through (ST) approaches, proposing a variety of ad-hoc rules for propagating gradients through non-differentiable activations and updating discrete weights. At the same time, ST methods can be truly derived as estimators in the stochastic binary network (SBN) model with Bernoulli weights. We advance these derivations to a more complete and systematic study. We analyze properties, estimation accuracy, obtain different forms of correct ST estimators for activations and weights, explain existing empirical approaches and their shortcomings, explain how latent weights arise from the mirror descent method when optimizing over probabilities. This allows to reintroduce ST methods, long known empirically, as sound approximations, apply them with clarity and develop further improvements.