human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "adversarial risk via optimal transport and optimal couplings"):
  Abstract: The accuracy of modern machine learning algorithms deteriorates severely on adversarially manipulated test data. Optimal adversarial risk quantifies the best error rate of any classifier in the presence of adversaries, and optimal adversarial classifiers are sought that minimize adversarial risk. In this paper, we investigate the optimal adversarial risk and optimal adversarial classifiers from an optimal transport perspective. We present a new and simple approach to show that the optimal adversarial risk for binary classification with $0-1$ loss function is completely characterized by an optimal transport cost between the probability distributions of the two classes, for a suitably defined cost function. We propose a novel coupling strategy that achieves the optimal transport cost for several univariate distributions like Gaussian, uniform and triangular. Using the optimal couplings, we obtain the optimal adversarial classifiers in these settings and show how they differ from optimal classifiers in the absence of adversaries. Based on our analysis, we evaluate algorithm-independent fundamental limits on adversarial risk for CIFAR-10, MNIST, Fashion-MNIST and SVHN datasets, and Gaussian mixtures based on them. In addition to the $0-1$ loss, we also derive bounds on the deviation of optimal risk and optimal classifier in the presence of adversaries for continuous loss functions, that are based on the convexity and smoothness of the loss functions.

Includes members:
  Member "lower bounds for adversarially robust pac learning":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "more data can expand the generalization gap between adversarially robust and standard models")
  Member "on the hardness of robust classification":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "randomization matters how to defend against strong adversarial attacks")
  Member "certified adversarial robustness via randomized smoothing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "overfitting in adversarially robust deep learning")
  Member "lower bounds on adversarial robustness from optimal transport":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "more data can expand the generalization gap between adversarially robust and standard models")
  Member "the curse of concentration in robust learning evasion and poisoning attacks from concentration of measure":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "utilizing network properties to detect erroneous inputs")
  Member "robustness via curvature regularization and vice versa":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "varmixup exploiting the latent space for robust training and inference")
  Member "adversarial spheres":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "utilizing network properties to detect erroneous inputs")
  Member "adversarial vulnerability for any classifier":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "utilizing network properties to detect erroneous inputs")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LG(Machine Learning)