Towards Accurate and Efficient Sub-8-Bit Integer Training

TL;DR

This paper explores sub-8-bit integer training from its essence of gradient descent optimization and achieves negligible accuracy loss across various neural networks and tasks and frees group quantization from inefficient memory rearrangement.

Abstract

Neural network training is a memory- and compute-intensive task. Quantization, which enables low-bitwidth formats in training, can significantly mitigate the workload. To reduce quantization error, recent methods have developed new data formats and additional pre-processing operations on quantizers. However, it remains quite challenging to achieve high accuracy and efficiency simultaneously. In this paper, we explore sub-8-bit integer training from its essence of gradient descent optimization. Our integer training framework includes two components: ShiftQuant to realize accurate gradient estimation, and L1 normalization to smoothen the loss landscape. ShiftQuant attains performance that approaches the theoretical upper bound of group quantization. Furthermore, it liberates group quantization from inefficient memory rearrangement. The L1 normalization facilitates the implementation of fully quantized normalization layers with impressive convergence accuracy. Our method frees sub-8-bit integer training from pre-processing and supports general devices. This framework achieves negligible accuracy loss across various neural networks and tasks ($0.92\%$ on 4-bit ResNets, $0.61\%$ on 6-bit Transformers). The prototypical implementation of ShiftQuant achieves more than $1.85\times/15.3\%$ performance improvement on CPU/GPU compared to its FP16 counterparts, and $33.9\%$ resource consumption reduction on FPGA than the FP16 counterparts. The proposed fully-quantized L1 normalization layers achieve more than $35.54\%$ improvement in throughout on CPU compared to traditional L2 normalization layers. Moreover, theoretical analysis verifies the advancement of our method.

Figures (18)

• Figure 1: Matrix multiplications in training. Inner dimensions are labeled in red.
• Figure 2: The difficulty of quantizing gradients comes from the diversity between channels. ShiftQuant aims to minimize the diversity through strategic grouping channels. (a) Gradients exhibit extremely bell-curve distribution, which is very difficult to quantize. (b) Diversity in magnitude of channels leads to high quantization error. (c) High diversity of channels in gradients. (d) ShiftQuant divides channels to several groups. Each group characters small diversity, leading to easier quantization.
• Figure 3: The power-of-two grouping strategy in ShiftQuant paves a way for implementing per-grouping quantization without memory rearrangement. Traditional implementation approach (b) focuses on applying off-the-peg packages. It transfers original matrix multiplication to several small matrix multiplications based on the grouping map $\bm{m}$, which involves expensive memory rearrangement. ShiftMM (c) aims higher hardware efficiency. It replaces the memory rearrangement with only a low-cost shift operation. Meanwhile, it only demands slight changes on off-the-peg packages.
• Figure 4: Low-precision networks feature sharpen loss landscape, which disrupts convergence. We visualize the loss landscape of ResNet20 on CIFAR10 by the method in visualizing-landscape.
• Figure 4: Results on Temporal Graph Network (TGN kumar2019predicting) .