Scaling Laws for Precision

Tanishq Kumar, Zachary Ankner, Benjamin Frederick Spector, Blake Bordelon, Niklas Muennighoff, Mansheej Paul, Cengiz Pehlevan, Christopher Re, Aditi Raghunathan

Keywords: quantization, scaling laws, precision, language models

TL;DR: We model the effects of precision on language model loss scaling, both during and after training. We find that overtrained models degrade more when quantized at inference time, and that training larger models in lower precision can be optimal.

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 can 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.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 12529