Deep neural networks are vulnerable to adversarial attacks and hard to interpret because of their black-box nature. The recently proposed invertible network is able to accurately reconstruct the inputs to a layer from its outputs, thus has the potential to unravel the black-box model. An invertible network classifier can be viewed as a two-stage model: (1) invertible transformation from input space to the feature space; (2) a linear classifier in the feature space. We can determine the decision boundary of a linear classifier in the feature space; since the transform is invertible, we can invert the decision boundary from the feature space to the input space. Furthermore, we propose to determine the projection of a data point onto the decision boundary, and define explanation as the difference between data and its projection. Finally, we propose to locally approximate a neural network with its first-order Taylor expansion, and define feature importance using a local linear model. We provide the implementation of our method: \url{https://github.com/juntang-zhuang/explain_invertible}.
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