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Adversarial examples form a major threat to incorporating machine learning (ML) models in critical applications. The existence and generalisation of these attacks have been attributed to the linear nature of ML models, deep neural network models in particular, in the high dimensional space. This paper presents a new nonlinear computational layer to the deep convolutional neural network architectures. This layer performs a set of comprehensive convolution operations that mimics the overall function of the human visual system (HVS) via focusing on learning structural information. The core of its computations is evaluating the components of the structural similarity metric (SSIM) in a setting that allows the kernels to learn to match structural information. The proposed SSIMLayer is inherently nonlinear. Experiments conducted on CIFAR-10 benchmark demonstrate that the SSIMLayer provides high learning capacity and shows more robustness against adversarial attacks.

SSIMLayer: Towards Robust Deep Representation Learning via Nonlinear Structural Similarity