2022/03/21 by Matteo Spallanzani, Spallanzani, Matteo, Gian Paolo Leonardi +3 · 1 citation
Computer Science · #Advanced Neural Network Applications #Computer Vision and Pattern Recognition (cs.CV) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.2203.11323
openalex publication_date 2022/03/21 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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.