Revisit, Extend, and Enhance Hessian-Free Influence Functions

TL;DR

This paper revisits the TracIn influence estimation method, providing insights into its effectiveness, extending its applications to fairness and robustness, and enhancing it with ensemble strategies for better performance in various deep learning tasks.

Contribution

It offers a deeper understanding of the simple Hessian approximation in TracIn, extends its use to fairness and robustness, and introduces an ensemble enhancement for improved influence estimation.

Findings

TracIn performs well despite its naive Hessian approximation.

The extended TracIn improves fairness and robustness in models.

Ensemble strategies enhance influence estimation accuracy.

Abstract

Influence functions serve as crucial tools for assessing sample influence in model interpretation, subset training set selection, noisy label detection, and more. By employing the first-order Taylor extension, influence functions can estimate sample influence without the need for expensive model retraining. However, applying influence functions directly to deep models presents challenges, primarily due to the non-convex nature of the loss function and the large size of model parameters. This difficulty not only makes computing the inverse of the Hessian matrix costly but also renders it non-existent in some cases. Various approaches, including matrix decomposition, have been explored to expedite and approximate the inversion of the Hessian matrix, with the aim of making influence functions applicable to deep models. In this paper, we revisit a specific, albeit naive, yet effective approximation method known as TracIn. This method substitutes the inverse of the Hessian matrix with an identity matrix. We provide deeper insights into why this simple approximation method performs well. Furthermore, we extend its applications beyond measuring model utility to include considerations of fairness and robustness. Finally, we enhance TracIn through an ensemble strategy. To validate its effectiveness, we conduct experiments on synthetic data and extensive evaluations on noisy label detection, sample selection for large language model fine-tuning, and defense against adversarial attacks.