Laplacian Power Networks: Bounding Indicator Function Smoothness for Adversarial Defense
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Deep Neural Networks often suffer from lack of robustness to adversarial noise. To mitigate this drawback, authors have proposed different approaches, such as adding regularizers or training using adversarial examples. In this paper we propose a new regularizer built upon the Laplacian of similarity graphs obtained from the representation of training data at each intermediate representation. This regularizer penalizes large changes (across consecutive layers in the architecture) in the distance between examples of different classes. We provide theoretical justification for this regularizer and demonstrate its effectiveness when facing adversarial noise on classical supervised learning vision datasets.
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