Neural gradients are near-lognormal: improved quantized and sparse training

TL;DR

This paper reveals that neural gradients follow a near-lognormal distribution and introduces two analytical methods to quantize and sparsify gradients, significantly reducing computational costs while maintaining accuracy.

Contribution

It is the first to quantize gradients to 6-bit floating-point and achieve up to 85% sparsity without accuracy loss, leveraging the lognormal distribution of gradients.

Findings

Gradient quantization to 6-bit floating-point achieves state-of-the-art results.

Gradient sparsity of up to 85% is achieved without accuracy degradation.

Proposed methods reduce computational and memory burdens effectively.

Abstract

While training can mostly be accelerated by reducing the time needed to propagate neural gradients back throughout the model, most previous works focus on the quantization/pruning of weights and activations. These methods are often not applicable to neural gradients, which have very different statistical properties. Distinguished from weights and activations, we find that the distribution of neural gradients is approximately lognormal. Considering this, we suggest two closed-form analytical methods to reduce the computational and memory burdens of neural gradients. The first method optimizes the floating-point format and scale of the gradients. The second method accurately sets sparsity thresholds for gradient pruning. Each method achieves state-of-the-art results on ImageNet. To the best of our knowledge, this paper is the first to (1) quantize the gradients to 6-bit floating-point formats, or (2) achieve up to 85% gradient sparsity -- in each case without accuracy degradation. Reference implementation accompanies the paper.