  Influence functions approximate the 'influences' of training data-points for
test predictions and have a wide variety of applications. Despite the
popularity, their computational cost does not scale well with model and
training data size. We present FastIF, a set of simple modifications to
influence functions that significantly improves their run-time. We use
k-Nearest Neighbors (kNN) to narrow the search space down to a subset of good
candidate data points, identify the configurations that best balance the
speed-quality trade-off in estimating the inverse Hessian-vector product, and
introduce a fast parallel variant. Our proposed method achieves about 80x
speedup while being highly correlated with the original influence values. With
the availability of the fast influence functions, we demonstrate their
usefulness in four applications. First, we examine whether influential
data-points can 'explain' test time behavior using the framework of
simulatability. Second, we visualize the influence interactions between
training and test data-points. Third, we show that we can correct model errors
by additional fine-tuning on certain influential data-points, improving the
accuracy of a trained MNLI model by 2.6% on the HANS challenge set using a
small number of gradient updates. Finally, we experiment with a
data-augmentation setup where we use influence functions to search for new
data-points unseen during training to improve model performance. Overall, our
fast influence functions can be efficiently applied to large models and
datasets, and our experiments demonstrate the potential of influence functions
in model interpretation and correcting model errors. Code is available at
https://github.com/salesforce/fast-influence-functions
