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Scaling Laws for Precision

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arxiv 2411.04330 v2 pith:UE2SBYHP submitted 2024-11-07 cs.LG cs.CL

classification cs.LGcs.CL
keywords traininglawsprecisionscalinginferencemodelmodelspretraining
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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Cited by 22 Pith papers

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