# Understanding Black-box Predictions via Influence Functions

arXiv: https://arxiv.org/abs/1703.04730 · HTML: https://mlsanity.com/paper/1703.04730/

## Key facts

- Cited by 1,741 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2017.

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## Abstract (arXiv)

How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data, thereby identifying training points most responsible for a given prediction. To scale up influence functions to modern machine learning settings, we develop a simple, efficient implementation that requires only oracle access to gradients and Hessian-vector products. We show that even on non-convex and non-differentiable models where the theory breaks down, approximations to influence functions can still provide valuable information. On linear models and convolutional neural networks, we demonstrate that influence functions are useful for multiple purposes: understanding model behavior, debugging models, detecting dataset errors, and even creating visually-indistinguishable training-set attacks.