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 "gans may have no nash equilibria"):
  Abstract: Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibrium solutions in the GAN zero-sum game. In this work, we show through several theoretical and numerical results that indeed GAN zero-sum games may not have any local Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We discuss several numerical experiments demonstrating the existence of proximal equilibrium solutions in GAN minimax problems.

Includes members:
  Member "what is local optimality in nonconvex nonconcave minimax optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "local nash equilibria are isolated strict local nash equilibria in almost all zero sum continuous games")
  Member "lipschitz generative adversarial nets":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "designing gans a likelihood ratio approach")
  Member "on gradient descent ascent for nonconvex concave minimax problems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "when can wasserstein gans minimize wasserstein distance")
  Member "policy optimization provably converges to nash equilibria in zero sum linear quadratic games":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "generative adversarial imitation learning with neural networks global optimality and convergence rate")
  Member "on finding local nash equilibria and only local nash equilibria in zero sum games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "inference based strategy alignment for general sum differential games")
  Member "sgd learns one layer networks in wgans":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "when can wasserstein gans minimize wasserstein distance")
  Member "on solving minimax optimization locally a follow the ridge approach":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "optimality and stability in non convex non concave min max optimization")
  Member "convergence of learning dynamics in stackelberg games":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "optimality and stability in non convex non concave min max optimization")

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)