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Cross-entropy is a widely used loss function in applications.
Theoretically principled trade-off between robustness and accuracy
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Application of the logistic function to bio-assay
Berkson, J · 1944
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Why I prefer logits to probits
Berkson, J · 1951
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A method for solving the convex programming problem with convergence rate o ( 1 / k 2 ) o(1/k^{2})
Nesterov, Y. E · 1983
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A decision-theoretic generalization of on-line learning and an application to boosting
Freund, Y. and Schapire, R. E · 1997
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Multi-class support vector machines
Weston, J. and Watkins, C · 1998
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Multicategory support vector machines: Theory and application to the classification of microarray data and satellite radiance data
Lee, Y., Lin, Y., and Wahba, G · 2004
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Convexity, classification, and risk bounds
Bartlett, P. L., Jordan, M. I., and McAuliffe, J. D · 2006
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Consistency of multiclass empirical risk minimization methods based on convex loss
Chen, D.-R. and Sun, T · 2006
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The consistency of multicategory support vector machines
Chen, D.-R. and Xiang, D.-H · 2006
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Fisher consistency of multicategory support vector machines
Liu, Y · 2007
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How to compare different loss functions and their risks
Steinwart, I · 2007
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On the consistency of multiclass classification methods
Tewari, A. and Bartlett, P. L · 2007
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Learning multiple layers of features from tiny images
Krizhevsky, A · 2009
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On the consistency of ranking algorithms
Duchi, J. C., Mackey, L. W., and Jordan, M. I · 2010
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Bag of tricks for adversarial training
Pang, T., Yang, X., Dong, Y., Su, H., and Zhu, J · 2010
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On the consistency of multi-label learning
Gao, W. and Zhou, Z.-H · 2011
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Reading digits in natural images with unsupervised feature learning
Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., and Ng, A. Y · 2011
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On NDCG consistency of listwise ranking methods
Ravikumar, P., Tewari, A., and Yang, E · 2011
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Consistent multilabel ranking through univariate losses
Dembczynski, K., Kotlowski, W., and Hüllermeier, E · 2012
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Imagenet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., and Hinton, G. E · 2012
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New analysis and algorithm for learning with drifting distributions
Mohri, M. and Medina, A. M · 2012
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Classification calibration dimension for general multiclass losses
Ramaswamy, H. G. and Agarwal, S · 2012
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Evasion attacks against machine learning at test time
Biggio, B., Corona, I., Maiorca, D., Nelson, B., Šrndić, N., Laskov, P., Giacinto, G., and Roli, F · 2013
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Consistency versus realizable H-consistency for multiclass classification
Long, P. and Servedio, R · 2013
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Cost-sensitive multiclass classification risk bounds
Pires, B. A., Szepesvari, C., and Ghavamzadeh, M · 2013
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Convex calibrated surrogates for low-rank loss matrices with applications to subset ranking losses
Ramaswamy, H. G., Agarwal, S., and Tewari, A · 2013
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Intriguing properties of neural networks
Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., and Fergus, R · 2013
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Explaining and harnessing adversarial examples
Goodfellow, I. J., Shlens, J., and Szegedy, C · 2014
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Multi-class deep boosting
Kuznetsov, V., Mohri, M., and Syed, U · 2014
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Sequence to sequence learning with neural networks
Sutskever, I., Vinyals, O., and Le, Q. V · 2014
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On consistent surrogate risk minimization and property elicitation
Agarwal, A. and Agarwal, S · 2015
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Learning and inference in the presence of corrupted inputs
Feige, U., Mansour, Y., and Schapire, R · 2015
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On the consistency of auc pairwise optimization
Gao, W. and Zhou, Z.-H · 2015
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Consistent multiclass algorithms for complex performance measures
Narasimhan, H., Ramaswamy, H., Saha, A., and Agarwal, S · 2015
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Consistent algorithms for multiclass classification with a reject option
Ramaswamy, H. G., Tewari, A., and Agarwal, S · 2015
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A consistent regularization approach for structured prediction
Ciliberto, C., Rosasco, L., and Rudi, A · 2016
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A unified view on multi-class support vector classification
Dogan, U., Glasmachers, T., and Igel, C · 2016
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Gaussian error linear units (gelus)
Hendrycks, D. and Gimpel, K · 2016
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Adversarial machine learning at scale
Kurakin, A., Goodfellow, I., and Bengio, S · 2016
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SGDR: Stochastic gradient descent with warm restarts
Loshchilov, I. and Hutter, F · 2016
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Multiclass classification calibration functions
Pires, B. Á. and Szepesvári, C · 2016
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Convex calibration dimension for multiclass loss matrices
Ramaswamy, H. G. and Agarwal, S · 2016
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Composite multiclass losses
Williamson, R. C., Vernet, E., and Reid, M. D · 2016
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Zagoruyko, S. and Komodakis, N · 2016
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Towards evaluating the robustness of neural networks
Carlini, N. and Wagner, D · 2017
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Robust loss functions under label noise for deep neural networks
Ghosh, A., Kumar, H., and Sastry, P. S · 2017
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Towards deep learning models resistant to adversarial attacks
Madry, A., Makelov, A., Schmidt, L., Tsipras, D., and Vladu, A · 2017
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On structured prediction theory with calibrated convex surrogate losses
Osokin, A., Bach, F., and Lacoste-Julien, S · 2017
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On the consistency of ordinal regression methods
Pedregosa, F., Bach, F., and Gramfort, A · 2017
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On theoretically optimal ranking functions in bipartite ranking
Uematsu, K. and Lee, Y · 2017
Adversarially robust distillation
Goldblum, M., Fowl, L., Feizi, S., and Goldstein, T · 2020
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Uncovering the limits of adversarial training against norm-bounded adversarial examples
Gowal, S., Qin, C., Uesato, J., Mann, T., and Kohli, P · 2020
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When nas meets robustness: In search of robust architectures against adversarial attacks
Guo, M., Yang, Y., Xu, R., Liu, Z., and Lin, D · 2020
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Discrepancy-based theory and algorithms for forecasting non-stationary time series
Kuznetsov, V. and Mohri, M · 2020
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Adversarial vertex mixup: Toward better adversarially robust generalization
Lee, S., Lee, H., and Yoon, S · 2020
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Adversarial examples from cryptographic pseudo-random generators
Bubeck, S., Lee, Y. T., Price, E., and Razenshteyn, I · 2018
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Curriculum adversarial training
Cai, Q.-Z., Liu, C., and Song, D · 2018
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Pac-learning in the presence of adversaries
Cullina, D., Bhagoji, A. N., and Mittal, P · 2018
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Robust inference for multiclass classification
Feige, U., Mansour, Y., and Schapire, R. E · 2018
Cited alongside, same era.
Averaging weights leads to wider optima and better generalization
Izmailov, P., Podoprikhin, D., Garipov, T., Vetrov, D. P., and Wilson, A. G · 2018
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Kannan, H., Kurakin, A., and Goodfellow, I · 2018
Cited alongside, same era.
Liu, A., Tang, S., Liu, X., Chen, X., Huang, L., Tu, Z., Song, D., and Tao, D · 2020
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Overfitting in adversarially robust deep learning
Rice, L., Wong, E., and Kolter, J. Z · 2020
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Weston-Watkins hinge loss and ordered partitions
Wang, Y. and Scott, C · 2020
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Improving adversarial robustness requires revisiting misclassified examples
Wang, Y., Zou, D., Yi, J., Bailey, J., Ma, X., and Gu, Q · 2020
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Fast is better than free: Revisiting adversarial training
Wong, E., Rice, L., and Kolter, J. Z · 2020
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Adversarial weight perturbation helps robust generalization
Wu, D., Xia, S.-T., and Wang, Y · 2020
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Intriguing properties of adversarial training at scale
Xie, C. and Yuille, A · 2020
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Dverge: diversifying vulnerabilities for enhanced robust generation of ensembles
Yang, H., Zhang, J., Dong, H., Inkawhich, N., Gardner, A., Touchet, A., Wilkes, W., Berry, H., and Li, H · 2020
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Bayes consistency vs. H-consistency: The interplay between surrogate loss functions and the scoring function class
Zhang, M. and Agarwal, S · 2020
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Adversarial examples in multi-layer random relu networks
Bartlett, P., Bubeck, S., and Cherapanamjeri, Y · 2021
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Sample complexity of robust linear classification on separated data
Bhattacharjee, R., Jha, S., and Chaudhuri, K · 2021
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A universal law of robustness via isoperimetry
Bubeck, S. and Sellke, M · 2021
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A single gradient step finds adversarial examples on random two-layers neural networks
Bubeck, S., Cherapanamjeri, Y., Gidel, G., and Tachet des Combes, R · 2021
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Surrogate regret bounds for polyhedral losses
Frongillo, R. and Waggoner, B · 2021
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Fat-shattering dimension of k k -fold maxima
Kontorovich, A. and Attias, I · 2021
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Adversarially robust learning with unknown perturbation sets
Montasser, O., Hanneke, S., and Srebro, N · 2021
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Improving model robustness with latent distribution locally and globally
Qian, Z., Zhang, S., Huang, K., Wang, Q., Zhang, R., and Yi, X · 2021
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Adversarial robustness with semi-infinite constrained learning
Robey, A., Chamon, L., Pappas, G., Hassani, H., and Ribeiro, A · 2021
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Formalizing generalization and robustness of neural networks to weight perturbations
Tsai, Y.-L., Hsu, C.-Y., Yu, C.-M., and Chen, P.-Y · 2021
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A pac-bayes analysis of adversarial robustness
Viallard, P., VIDOT, E. G., Habrard, A., and Morvant, E · 2021
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Adversarially robust estimate and risk analysis in linear regression
Xing, Y., Zhang, R., and Cheng, G · 2021
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Adversarially robust learning of real-valued functions
Attias, I. and Hanneke, S · 2022
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Generalizing consistent multi-class classification with rejection to be compatible with arbitrary losses
Cao, Y., Cai, T., Feng, L., Gu, L., Gu, J., An, B., Niu, G., and Sugiyama, M · 2022
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Cat: Customized adversarial training for improved robustness
Cheng, M., Lei, Q., Chen, P. Y., Dhillon, I., and Hsieh, C. J · 2022
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Mma training: Direct input space margin maximization through adversarial training
Ding, G. W., Sharma, Y., Lui, K. Y. C., and Huang, R · 2022
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An embedding framework for the design and analysis of consistent polyhedral surrogates
Finocchiaro, J., Frongillo, R. M., and Waggoner, B · 2022
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Fast provably robust decision trees and boosting
Guo, J.-Q., Teng, M.-Z., Gao, W., and Zhou, Z.-H · 2022
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Enhancing adversarial training with second-order statistics of weights
Jin, G., Yi, X., Huang, W., Schewe, S., and Huang, X · 2022
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Domain invariant adversarial learning
Levi, M., Attias, I., and Kontorovich, A · 2022
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Towards consistency in adversarial classification
Meunier, L., Ettedgui, R., Pinot, R., Chevaleyre, Y., and Atif, J · 2022
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Transductive robust learning guarantees
Montasser, O., Hanneke, S., and Srebro, N · 2022
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The structured abstain problem and the lovász hinge
Nueve, E. B., Frongillo, R., and Finocchiaro, J. J · 2022
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Consistent polyhedral surrogates for top-k classification and variants
Thilagar, A., Frongillo, R., Finocchiaro, J. J., and Goodwill, E · 2022
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Stability analysis and generalization bounds of adversarial training
Xiao, J., Fan, Y., Sun, R., Wang, J., and Luo, Z.-Q · 2022
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The adversarial consistency of surrogate risks for binary classification
Frank, N. and Niles-Weed, J · 2023
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On achieving optimal adversarial test error
Li, J. D. and Telgarsky, M · 2023
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ℋ {\mathscr{H}} -consistency bounds for pairwise misranking loss surrogates
Mao, A., Mohri, M., and Zhong, Y · 2023
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On classification-calibration of gamma-phi losses
Wang, Y. and Scott, C. D · 2023
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Revisiting discriminative vs. generative classifiers: Theory and implications
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