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

TL;DR

This paper introduces Semi-Relaxed Quantization with DropBits, a novel approach for training low-bit neural networks that reduces bias and variance in quantization, enabling more efficient deployment on resource-limited devices.

Contribution

The paper proposes Semi-Relaxed Quantization with DropBits, a new method combining multi-class straight-through estimator and bit-dropping regularization to improve low-bit neural network training.

Findings

Semi-Relaxed Quantization outperforms Gumbel-Softmax based methods.

DropBits effectively reduces bias in quantization.

Learning heterogeneous quantization levels improves performance.

Abstract

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