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Network quantization, which aims to reduce the bit-lengths of the networkweights and activations, has emerged as one of the key ingredients to reducethe size of neural networks for their deployments to resource-limited devices.In order to overcome the nature of transforming continuous activations andweights to discrete ones, recent study called Relaxed Quantization (RQ)[Louizos et al. 2019] successfully employ the popular Gumbel-Softmax thatallows this transformation with efficient gradient-based optimization. However,RQ with this Gumbel-Softmax relaxation still suffers from bias-variancetrade-off depending on the temperature parameter of Gumbel-Softmax. To resolvethe issue, we propose a novel method, Semi-Relaxed Quantization (SRQ) that usesmulti-class straight-through estimator to effectively reduce the bias andvariance, along with a new regularization technique, DropBits that replacesdropout regularization to randomly drop the bits instead of neurons to furtherreduce the bias of the multi-class straight-through estimator in SRQ. As anatural extension of DropBits, we further introduce the way of learningheterogeneous quantization levels to find proper bit-length for each layerusing DropBits. We experimentally validate our method on various benchmarkdatasets and network architectures, and also support the quantized lotteryticket hypothesis: learning heterogeneous quantization levels outperforms thecase using the same but fixed quantization levels from scratch.

Semi-Relaxed Quantization with DropBits: Training Low-Bit Neural Networks via Bit-wise Regularization