Training Quantised Neural Networks with STE Variants: the Additive Noise Annealing Algorithm

TL;DR

This paper analyzes various STE variants for training quantised neural networks, providing a theoretical framework, and introduces the additive noise annealing algorithm that improves training by synchronizing regularisations across layers.

Contribution

It offers a rigorous analysis of STE variants, models them as stochastic regularisations, and proposes the ANA algorithm to enhance QNN training based on these insights.

Findings

ANA improves CIFAR-10 accuracy by proper STE synchronization

Most STE variants can be modelled as stochastic stair function regularisations

Synchronisation of layer regularisations is crucial for convergence

Abstract

Training quantised neural networks (QNNs) is a non-differentiable optimisation problem since weights and features are output by piecewise constant functions. The standard solution is to apply the straight-through estimator (STE), using different functions during the inference and gradient computation steps. Several STE variants have been proposed in the literature aiming to maximise the task accuracy of the trained network. In this paper, we analyse STE variants and study their impact on QNN training. We first observe that most such variants can be modelled as stochastic regularisations of stair functions; although this intuitive interpretation is not new, our rigorous discussion generalises to further variants. Then, we analyse QNNs mixing different regularisations, finding that some suitably synchronised smoothing of each layer map is required to guarantee pointwise compositional convergence to the target discontinuous function. Based on these theoretical insights, we propose additive noise annealing (ANA), a new algorithm to train QNNs encompassing standard STE and its variants as special cases. When testing ANA on the CIFAR-10 image classification benchmark, we find that the major impact on task accuracy is not due to the qualitative shape of the regularisations but to the proper synchronisation of the different STE variants used in a network, in accordance with the theoretical results.