Scaling Laws for Precision

introduces "precision-aware" scaling laws that predict how model performance is affected by both training and inference precision in LLMs; key findings include: 1) post-training quantization becomes more harmful as models are trained on more data, eventually making additional pretraining actively detrimental, 2) training in lower precision requires increasing model size to maintain performance, and 3) when jointly optimizing model size, data, and precision, the compute-optimal training precision is around 7-8 bits and independent of compute; also reports that when the model size is fixed, compute-optimal precision increases approximately logarithmically with data; the authors validate their predictions on models up to 1.7B parameters trained on up to 26B tokens, showing that both very high (16-bit) and very low (sub 4-bit) training precisions may be suboptimal.