Scaling Laws for Floating Point Quantization Training

TL;DR

This paper develops a comprehensive scaling law for floating-point quantization in large language model training, revealing optimal bit configurations and data size effects to improve efficiency and performance.

Contribution

It introduces an accurate unified scaling law for FP quantization in LLM training and offers practical guidelines for hardware and training optimization.

Findings

Exponent bits slightly more impactful than mantissa bits

Critical data size limits low-precision training degradation

Optimal FP quantization precision between 4-8 bits

Abstract

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point (FP) quantization, and thus cannot well fit the LLM losses in this scenario. In contrast, while FP quantization training is more commonly implemented in production, it's research has been relatively superficial. In this paper, we thoroughly explore the effects of FP quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in FP quantization training performance of LLM models. In addition to an accurate FP quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal FP quantization precision is directly proportional to the computational power, but within a wide computational power range. We estimate that the best cost-performance precision should lie between 4-8 bits.