  Despite advancements, fine-tuning Large Language Models (LLMs) remains costly
due to the extensive parameter count and substantial data requirements for
model generalization. Accessibility to computing resources remains a barrier
for the open-source community. To address this challenge, we propose the
In2Core algorithm, which selects a coreset by analyzing the correlation between
training and evaluation samples with a trained model. Notably, we assess the
model's internal gradients to estimate this relationship, aiming to rank the
contribution of each training point. To enhance efficiency, we propose an
optimization to compute influence functions with a reduced number of layers
while achieving similar accuracy. By applying our algorithm to instruction
fine-tuning data of LLMs, we can achieve similar performance with just 50% of
the training data. Meantime, using influence functions to analyze model
coverage to certain testing samples could provide a reliable and interpretable
signal on the training set's coverage of those test points.
