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arXiv · 1905.10452

Additive Noise Annealing and Approximation Properties of Quantized Neural Networks

Matteo Spallanzani·Lukas Cavigelli·Gian Paolo Leonardi·Marko Bertogna·Luca Benini
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Abstract

We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in particular that any Lipschitz-continuous map defined on a hypercube can be uniformly approximated by a quantized neural network. We then focus on the regularization effect of additive noise on the arguments of multi-step functions inherent to the quantization of continuous variables. In particular, when the expectation operator is applied to a non-differentiable multi-step random function, and if the underlying probability density is differentiable (in either classical or weak sense), then a differentiable function is retrieved, with explicit bounds on its Lipschitz constant. Based on these results, we propose a novel gradient-based training algorithm for quantized neural networks that generalizes the straight-through estimator, acting on noise applied to the network's parameters. We evaluate our algorithm on the CIFAR-10 and ImageNet image classification benchmarks, showing state-of-the-art performance on AlexNet and MobileNetV2 for ternary networks.

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Matteo Spallanzani, Lukas Cavigelli, Gian Paolo Leonardi, Marko Bertogna, Luca Benini. 2019-05-24. Additive Noise Annealing and Approximation Properties of Quantized Neural Networks. https://arxiv.org/abs/1905.10452

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