  Influence functions approximate the effect of training samples in test-time
predictions and have a wide variety of applications in machine learning
interpretability and uncertainty estimation. A commonly-used (first-order)
influence function can be implemented efficiently as a post-hoc method
requiring access only to the gradients and Hessian of the model. For linear
models, influence functions are well-defined due to the convexity of the
underlying loss function and are generally accurate even across difficult
settings where model changes are fairly large such as estimating group
influences. Influence functions, however, are not well-understood in the
context of deep learning with non-convex loss functions. In this paper, we
provide a comprehensive and large-scale empirical study of successes and
failures of influence functions in neural network models trained on datasets
such as Iris, MNIST, CIFAR-10 and ImageNet. Through our extensive experiments,
we show that the network architecture, its depth and width, as well as the
extent of model parameterization and regularization techniques have strong
effects in the accuracy of influence functions. In particular, we find that (i)
influence estimates are fairly accurate for shallow networks, while for deeper
networks the estimates are often erroneous; (ii) for certain network
architectures and datasets, training with weight-decay regularization is
important to get high-quality influence estimates; and (iii) the accuracy of
influence estimates can vary significantly depending on the examined test
points. These results suggest that in general influence functions in deep
learning are fragile and call for developing improved influence estimation
methods to mitigate these issues in non-convex setups.
