Optimal Transport, also known as Wasserstein distance or Kantorovich-Rubinstein distance, is a mathematical framework that deals with the optimal way to transport mass from one distribution to another. It has applications in various fields, including probability theory, economics, and image processing. The central idea is to determine the most efficient way to transform one probability distribution into another while minimizing the total “cost” or “distance” of transportation.

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Towards Robustness of Deep Neural Networks via Networks via Regularization

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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.

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Domain oriented Language Modeling with Adaptive Hybrid Masking and Optimal Transport Alignment

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Motivated by the success of pre-trained language models such as BERT in a broad range of natural language processing (NLP) tasks, recent research efforts have been made for adapting these models for different application domains. Along this line, existing domain-oriented models have primarily followed the vanilla BERT architecture and have a straightforward use of the domain corpus. However, domain-oriented tasks usually require accurate understanding of domain phrases, and such fine-grained phrase-level knowledge is hard to be captured by existing pre-training scheme. Also, the word co-occurrences guided semantic learning of pre-training models can be largely augmented by entity-level association knowledge. But meanwhile, there is a risk of introducing noise due to the lack of ground truth word-level alignment. To address the issues, we provide a generalized domain-oriented approach, which leverages auxiliary domain knowledge to improve the existing pre-training framework from two aspects. First, to preserve phrase knowledge effectively, we build a domain phrase pool as auxiliary knowledge, meanwhile we introduce Adaptive Hybrid Masked Model to incorporate such knowledge. It integrates two learning modes, word learning and phrase learning, and allows them to switch between each other. Second, we introduce Cross Entity Alignment to leverage entity association as weak supervision to augment the semantic learning of pre-trained models. To alleviate the potential noise in this process, we introduce an interpretable Optimal Transport based approach to guide alignment learning. Experiments on four domain-oriented tasks demonstrate the superiority of our framework.

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Optimal Transport Classifier: Defending Against Adversarial Attacks by Regularized Deep Embedding

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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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