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For the past few years, Deep Neural Network (DNN) robustness has become aquestion of paramount importance. As a matter of fact, in sensitive settingsmisclassification can lead to dramatic consequences. Such misclassificationsare likely to occur when facing adversarial attacks, hardware failures orlimitations, and imperfect signal acquisition. To address this question,authors have proposed different approaches aiming at increasing the robustnessof DNNs, such as adding regularizers or training using noisy examples. In thispaper we propose a new regularizer built upon the Laplacian of similaritygraphs obtained from the representation of training data at each layer of theDNN architecture. This regularizer penalizes large changes (across consecutivelayers in the architecture) in the distance between examples of differentclasses, and as such enforces smooth variations of the class boundaries. Sinceit is agnostic to the type of deformations that are expected when predictingwith the DNN, the proposed regularizer can be combined with existing ad-hocmethods. We provide theoretical justification for this regularizer anddemonstrate its effectiveness to improve robustness of DNNs on classicalsupervised learning vision datasets.

Laplacian Networks: Bounding Indicator Function Smoothness for Neural Network Robustness