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Important insights towards the explainability of neural networks reside inthe characteristics of their decision boundaries. In this work, we borrow toolsfrom the field of adversarial robustness, and propose a new perspective thatrelates dataset features to the distance of samples to the decision boundary.This enables us to carefully tweak the position of the training samples andmeasure the induced changes on the boundaries of CNNs trained on large-scalevision datasets. We use this framework to reveal some intriguing properties ofCNNs. Specifically, we rigorously confirm that neural networks exhibit a highinvariance to non-discriminative features, and show that the decisionboundaries of a DNN can only exist as long as the classifier is trained withsome features that hold them together. Finally, we show that the constructionof the decision boundary is extremely sensitive to small perturbations of thetraining samples, and that changes in certain directions can lead to suddeninvariances in the orthogonal ones. This is precisely the mechanism thatadversarial training uses to achieve robustness.

Hold me tight! Influence of discriminative features on deep network boundaries