Error Diffusion: Post Training Quantization with Block-Scaled Number Formats for Neural Networks

TL;DR

This paper introduces error diffusion, a post-training quantization method that supports block-scaled number formats, improving neural network deployment by reducing hardware costs while maintaining output quality.

Contribution

It presents a hyperparameter-free, error diffusion approach for post-training quantization with block-scaled formats, without relying on backpropagation or Hessian information.

Findings

Consistently improves quantization performance across various architectures.

Demonstrates robustness of block-scaled formats in neural network quantization.

Provides an open-source library for emulating number formats in PyTorch.

Abstract

Quantization reduces the model's hardware costs, such as data movement, storage, and operations like multiply and addition. It also affects the model's behavior by degrading the output quality. Therefore, there is a need for methods that preserve the model's behavior when quantizing model parameters. More exotic numerical encodings, such as block-scaled number formats, have shown advantages for utilizing a fixed bit budget to encode model parameters. This paper presents error diffusion (ED), a hyperparameter-free method for post-training quantization with support for block-scaled data formats. Our approach does not rely on backpropagation or Hessian information. We describe how to improve the quantization process by viewing the neural model as a composite function and diffusing the quantization error in every layer. In addition, we introduce TensorCast, an open-source library based on PyTorch to emulate a variety of number formats, including the block-scaled ones, to aid the research in neural model quantization. We demonstrate the efficacy of our algorithm through rigorous testing on various architectures, including vision and large language models (LLMs), where it consistently delivers competitive results. Our experiments confirm that block-scaled data formats provide a robust choice for post-training quantization and could be used effectively to enhance the practical deployment of advanced neural networks.