[Paper Review] Scalable Methods for 8-bit Training of Neural Networks

Ron Banner, Itay Hubara+2 more|arXiv (Cornell University)|May 25, 2018

Advanced Neural Network Applications25 references129 citations

TL;DR

Demonstrates that training neural networks entirely in 8-bit is feasible by using Range Batch-Normalization and Gradients Bifurcation, achieving ImageNet-scale results without accuracy loss.

ABSTRACT

Quantized Neural Networks (QNNs) are often used to improve network efficiency during the inference phase, i.e. after the network has been trained. Extensive research in the field suggests many different quantization schemes. Still, the number of bits required, as well as the best quantization scheme, are yet unknown. Our theoretical analysis suggests that most of the training process is robust to substantial precision reduction, and points to only a few specific operations that require higher precision. Armed with this knowledge, we quantize the model parameters, activations and layer gradients to 8-bit, leaving at a higher precision only the final step in the computation of the weight gradients. Additionally, as QNNs require batch-normalization to be trained at high precision, we introduce Range Batch-Normalization (BN) which has significantly higher tolerance to quantization noise and improved computational complexity. Our simulations show that Range BN is equivalent to the traditional batch norm if a precise scale adjustment, which can be approximated analytically, is applied. To the best of the authors' knowledge, this work is the first to quantize the weights, activations, as well as a substantial volume of the gradients stream, in all layers (including batch normalization) to 8-bit while showing state-of-the-art results over the ImageNet-1K dataset.

Motivation & Objective

• Motivate quantized training to reduce computation and memory during training.
• Propose 8-bit quantization for weights, activations, and most gradients while preserving accuracy.
• Address numerical stability bottlenecks in batch normalization and backpropagation.
• Introduce Range Batch-Normalization as a low-precision alternative to standard BN.
• Demonstrate practical training of large models (ImageNet) with quantized back-propagation.

Proposed method

• Replace batch normalization with Range BN to tolerate quantization and avoid high-precision square-root operations.
• Quantize weights, activations, and a substantial portion of gradients to 8-bit, keeping weight-gradient computation in 16-bit.
• Introduce Gradients Bifurcation: compute layer gradients g_l at 8-bit for the backward pass while computing g_W at 16-bit for updates in parallel.
• Use stochastic rounding for gradient quantization to ensure unbiased accumulation of updates.
• Apply GEMMLOWP quantization scheme for training-time quantization.
• Adopt Straight-Through Estimator (STE) for discrete-variable differentiation during backpropagation.

Experimental results

Research questions

• RQ1 Can 8-bit quantization be applied across weights, activations, and most gradients during training without degrading accuracy on large-scale datasets?
• RQ2 How can batch normalization and gradient computations be adapted to low precision to maintain stability and performance?
• RQ3 Does Range Batch-Normalization provide comparable accuracy to standard BN under low-precision training?
• RQ4 What is the impact of quantized back-propagation on training speed, memory, and energy efficiency?

Key findings

• Range BN can approximate standard batch normalization, yielding comparable accuracy in experiments on ImageNet (e.g., ResNet-50) and CIFAR-10.
• Most of the training computations can be performed at 8-bit, with only the final weight-gradient update and a 16-bit copy of layer gradients remaining at higher precision.
• Gradients bifurcation (8-bit g_l and 16-bit g_W) enables efficient backpropagation without harming convergence.
• Quantized back-propagation with 8-bit activations/weights and 16-bit gradient copy achieves training with no loss in accuracy on ImageNet for the tested models.
• Stochastic rounding is essential for convergent training under quantization of gradients.
• Range BN and 8-bit training offer significant hardware efficiency benefits (faster MACs, lower energy) compared to full-precision training.