Approximating Language Model Training Data from Weights

Modern language models often have open weights but closed training data. We formalize the problem of data approximation from model weights and propose several baselines and metrics. We develop a gradient-based approach that selects the highest-matching data from a large public text corpus and show its effectiveness at recovering useful data given only weights of the original and finetuned models. Even when none of the true training data is known, our method is able to locate a small subset of public Web documents can be used to train a model to close to the original model performance given models trained for both classification and supervised-finetuning. On the AG News classification task, our method improves performance from 65% (using randomly selected data) to 80%, approaching the expert benchmark of 88%. When applied to a model trained with SFT on MSMARCO web documents, our method reduces perplexity from 3.3 to 2.3, compared to an expert LLAMA model's perplexity of 2.0.

Compute-Constrained Data Selection

Data selection can reduce the amount of training data needed to finetune LLMs; however, the efficacy of data selection scales directly with its compute. Motivated by the practical challenge of compute-constrained finetuning, we consider the setting in which both the cost of selecting data and training are budgeted for. We first formalize the problem of data selection with a cost-aware utility function, and model the data selection problem as trading off initial-selection cost for training gain. We run a comprehensive sweep of experiments across multiple tasks, varying compute budget by scaling finetuning tokens, model sizes, and data selection compute. These experiments show the validity of this model in real-world experiments. Interestingly we find that many powerful data selection methods are almost never compute-optimal, and that cheaper data selection alternatives dominate both from a theoretical and empirical perspective.