Title: INTERPRETATION OF NEURAL NETWORK IS FRAGILE. Abstract: In order for machine learning to be deployed and trusted in many applications, it is crucial to be able to reliably explain why the machine learning algorithm makes certain predictions. For example, if an algorithm classifies a given pathology image to be a malignant tumor, then the doctor may need to know which parts of the image led the algorithm to this classification. How to interpret black-box predictors is thus an important and active area of research.  A fundamental question is: how much can we trust the interpretation itself? In this paper, we show that interpretation of deep learning predictions is extremely fragile in the following sense:  two perceptively indistinguishable inputs with the same predicted label can be assigned very different}interpretations. We systematically characterize the fragility of the interpretations generated by several widely-used feature-importance interpretation methods (saliency maps, integrated gradient, and DeepLIFT) on ImageNet and CIFAR-10. Our experiments show that even small random perturbation can change the feature importance and new systematic perturbations can lead to dramatically different interpretations without changing the label. We extend these results to show that interpretations based on exemplars (e.g. influence functions) are similarly fragile. Our analysis of the geometry of the Hessian matrix gives insight on why fragility could be a fundamental challenge to the current interpretation approaches.