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We apply concepts from manifold regularization to develop new regularization techniques for training locally stable deep neural networks.
A technique for the numerical solution of certain integral equations of the first kind
David L Phillips · 1962
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From graphs to manifolds–weak and strong pointwise consistency of graph laplacians
Matthias Hein, Jean-Yves Audibert, and Ulrike Von Luxburg · 2005
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Linear manifold regularization for large scale semi-supervised learning
Vikas Sindhwani, Partha Niyogi, Mikhail Belkin, and Sathiya Keerthi · 2005
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Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
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Towards a theoretical foundation for laplacian-based manifold methods
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Graph laplacians and their convergence on random neighborhood graphs
Matthias Hein, Jean-Yves Audibert, and Ulrike von Luxburg · 2007
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Large-scale sparsified manifold regularization
Ivor W Tsang and James T Kwok · 2007
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Online manifold regularization: A new learning setting and empirical study
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Consistency of spectral clustering
Ulrike Von Luxburg, Mikhail Belkin, and Olivier Bousquet · 2008
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Discriminative semi-supervised feature selection via manifold regularization
Zenglin Xu, Irwin King, Michael Rung-Tsong Lyu, and Rong Jin · 2010
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Spectral sparsification of graphs
Daniel A Spielman and Shang-Hua Teng · 2011
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Ensemble manifold regularization
Bo Geng, Dacheng Tao, Chao Xu, Linjun Yang, and Xian-Sheng Hua · 2012
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Manifold regularization and semi-supervised learning: Some theoretical analyses
Partha Niyogi · 2013
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Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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Numerical methods for the solution of ill-posed problems , volume 328
Andrei Nikolaevich Tikhonov, AV Goncharsky, VV Stepanov, and Anatoly G Yagola · 2013
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Explaining and harnessing adversarial examples, 2014
Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
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Manifold regularized deep neural networks
Vikrant Singh Tomar and Richard C Rose · 2014
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Nicholas Carlini, Anish Athalye, Nicolas Papernot, Wieland Brendel, Jonas Rauber, Dimitris Tsipras, Ian Goodfellow, Aleksander Madry, and Alexey Kurakin · 2019
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Unlabeled data improves adversarial robustness, 2019
Yair Carmon, Aditi Raghunathan, Ludwig Schmidt, Percy Liang, and John C. Duchi · 2019
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Minimally distorted adversarial examples with a fast adaptive boundary attack, 2019
Francesco Croce and Matthias Hein · 2019
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Using pre-training can improve model robustness and uncertainty, 2019
Dan Hendrycks, Kimin Lee, and Mantas Mazeika · 2019
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Tianyu Pang, Kun Xu, Yinpeng Dong, Chao Du, Ning Chen, and Jun Zhu · 2019
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A convex relaxation barrier to tight robustness verification of neural networks
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Adversarial training for free!, 2019
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Are labels required for improving adversarial robustness?, 2019
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Wasserstein adversarial examples via projected sinkhorn iterations, 2019
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Training for faster adversarial robustness verification via inducing relu stability
Kai Xiao, Vincent Tjeng, Nur Muhammad Shafiullah, and Aleksander Madry · 2019
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Theoretically principled trade-off between robustness and accuracy, 2019
Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, and Michael I. Jordan · 2019
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Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks, 2020
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