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arXiv · 2410.07064

Data Selection via Optimal Control for Language Models

Yuxian Gu·Li Dong·Hongning Wang·Yaru Hao·Qingxiu Dong·Furu Wei·Minlie Huang
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Abstract

This work investigates the selection of high-quality pre-training data from massive corpora to enhance LMs' capabilities for downstream usage. We formulate data selection as a generalized Optimal Control problem, which can be solved theoretically by Pontryagin's Maximum Principle (PMP), yielding a set of necessary conditions that characterize the relationship between optimal data selection and LM training dynamics. Based on these theoretical results, we introduce PMP-based Data Selection (PDS), a framework that approximates optimal data selection by solving the PMP conditions. In our experiments, we adopt PDS to select data from CommmonCrawl and show that the PDS-selected corpus accelerates the learning of LMs and constantly boosts their performance on a wide range of downstream tasks across various model sizes. Moreover, the benefits of PDS extend to ~400B models trained on ~10T tokens, as evidenced by the extrapolation of the test loss curves according to the Scaling Laws. PDS also improves data utilization when the pre-training data is limited, by reducing the data demand by 1.8 times, which helps mitigate the quick exhaustion of available web-crawled corpora. Our code, model, and data can be found at https://github.com/microsoft/LMOps/tree/main/data_selection.

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Yuxian Gu, Li Dong, Hongning Wang, Yaru Hao, Qingxiu Dong, Furu Wei, Minlie Huang. 2025-03-18. Data Selection via Optimal Control for Language Models. https://arxiv.org/abs/2410.07064

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