Scaling Laws for Precision

TL;DR

This paper develops 'precision-aware' scaling laws that predict how low precision training and inference impact language model quality and cost, enabling better optimization of model size, data, and precision choices.

Contribution

It introduces unified scaling laws accounting for low precision effects during training and inference, validated on extensive pretraining data and larger models.

Findings

Lower precision reduces effective parameter count and increases loss predictability.

Post-training quantization degradation grows with more training data, potentially harming model performance.

Training larger models in lower precision can be more compute-efficient.

Abstract

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose that training in lower precision reduces the model's "effective parameter count," allowing us to predict the additional loss incurred from training in low precision and post-train quantization. For inference, we find that the degradation introduced by post-training quantization increases as models are trained on more data, eventually making additional pretraining data actively harmful. For training, our scaling laws allow us to predict the loss of a model with different parts in different precisions, and suggest that training larger models in lower precision may be compute optimal. We unify the scaling laws for post and pretraining quantization to arrive at a single functional form that predicts degradation from training and inference in varied precisions. We fit on over 465 pretraining runs and validate our predictions on model sizes up to 1.7B parameters trained on up to 26B tokens.