Efficient Data Selection at Scale via Influence Distillation
Authors: name: Mahdi Nikdan, name: Vincent Cohen-Addad, name: Dan Alistarh, name: Vahab Mirrokni

Effective data selection is critical for efficient training of modern Large
Language Models (LLMs). This paper introduces Influence Distillation, a novel,
mathematically-justified framework for data selection that employs second-order
information to optimally weight training samples. By distilling each sample's
influence on a target distribution, our method assigns model-specific weights
that are used to select training data for LLM fine-tuning, guiding it toward
strong performance on the target domain. We derive these optimal weights for
both Gradient Descent and Adam optimizers. To ensure scalability and reduce
computational cost, we propose a landmark-based approximation:
influence is precisely computed for a small subset of "landmark" samples and
then efficiently propagated to all other samples to determine their weights. We
validate Influence Distillation by applying it to instruction tuning on the
Tulu V2 dataset, targeting a range of tasks including GSM8k, SQuAD, and MMLU,
across several models from the Llama and Qwen families. Experiments show that
Influence Distillation matches or outperforms state-of-the-art performance
while achieving up to 3.5times faster selection.