Towards Robustness of Deep Neural Networks via Networks via Regularization Recent studies have demonstrated the vulnerability of deep neural networks against adversarial examples. In-spired by the observation that adversarial examples often lie outside the natural image data manifold and the intrinsic dimension of image data is much smaller than its pixel space dimension, we propose to embed high-dimensional input images into a low-dimensional space and apply regularization on the embedding space to push the adversarial examples back to the manifold. The proposed framework is called Embedding Regularized Classifier (ER-Classifier), which improves the adversarial robustness of the classifier through embedding regularization. Besides improving classification accuracy against adversarial examples, the framework can be combined with detection methods to detect adversarial examples. Experimental results on several benchmark datasets show that, our proposed framework achieves good performance against strong adversarial at-tack methods.
Deep Embedding refers to the process of learning a meaningful representation (embedding) of data using a deep neural network. This representation is typically lower-dimensional and captures important features or characteristics of the input data. Deep embeddings are commonly used in tasks like classification, clustering, and visualization.
Self-Attentive Attributed Network Embedding Through Adversarial Learning Network embedding aims to learn the low-dimensional representations/embeddings of vertices which preserve the structure and inherent properties of the networks. The resultant embeddings are beneficial to downstream tasks such as vertex classification and link prediction. A vast majority of real-world networks are coupled with a rich set of vertex attributes, which could be potentially complementary in learning better embeddings. Existing attributed network embedding models, with shallow or deep architectures, typically seek to match the representations in topology space and attribute space for each individual vertex by assuming that the samples from the two spaces are drawn uniformly. The assumption, however, can hardly be guaranteed in practice. Due to the intrinsic sparsity of sampled vertex sequences and incompleteness in vertex attributes, the discrepancy between the attribute space and the network topology space inevitably exists. Furthermore, the interactions among vertex attributes, a.k.a cross features, have been largely ignored by existing approaches. To address the above issues, in this paper, we propose Nettention, a self-attentive network embedding approach that can efficiently learn vertex embeddings on attributed network. Instead of sample-wise optimization, Nettention aggregates the two types of information through minimizing the difference between the representation distributions in the low-dimensional topology and attribute spaces. The joint inference is encapsulated in a generative adversarial training process, yielding better generalization performance and robustness. The learned distributions consider both locality-preserving and global reconstruction constraints which can be inferred from the learning of the adversarially regularized autoencoders. Additionally, a multi-head self-attention module is developed to explicitly model the attribute interactions. Extensive experiments on benchmark datasets have verified the effectiveness of the proposed Nettention model on a variety of tasks, including vertex classification and link prediction.
Optimal Transport Classifier: Defending Against Adversarial Attacks by Regularized Deep Embedding Recent studies have demonstrated the vulnerability of deep convolutional neural networks against adversarial examples. Inspired by the observation that the intrinsic dimension of image data is much smaller than its pixel space dimension and the vulnerability of neural networks grows with the input dimension, we propose to embed high-dimensional input images into a low-dimensional space to perform classification. However, arbitrarily projecting the input images to a low-dimensional space without regularization will not improve the robustness of deep neural networks. Leveraging optimal transport theory, we propose a new framework, Optimal Transport Classifier (OT-Classifier), and derive an objective that minimizes the discrepancy between the distribution of the true label and the distribution of the OT-Classifier output. Experimental results on several benchmark datasets show that, our proposed framework achieves state-of-the-art performance against strong adversarial attack methods.
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