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

arXiv: https://arxiv.org/abs/2006.08173 · HTML: https://mlsanity.com/paper/2006.08173/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Accurate Neural Training with 4-bit Matrix Multiplications at Standard Formats](https://mlsanity.com/paper/2112.10769/) (2021)
- [Minimum Variance Unbiased N:M Sparsity for the Neural Gradients](https://mlsanity.com/paper/2203.10991/) (2022)
- [Bimodal Distributed Binarized Neural Networks](https://mlsanity.com/paper/2204.02004/) (2022)
- [Adaptive Gradient Regularization: A Faster and Generalizable Optimization Technique for Deep Neural Networks](https://mlsanity.com/paper/2407.16944/) (2024)

## Abstract (arXiv)

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.