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 "a tight and unified analysis of extragradient for a whole spectrum of differentiable games"):
  Abstract: We consider differentiable games: multi-objective minimization problems, where the goal is to find a Nash equilibrium. The machine learning community has recently started using extrapolation-based variants of the gradient method. A prime example is the extragradient, which yields linear convergence in cases like bilinear games, where the standard gradient method fails. The full benefits of extrapolation-based methods are not known: i) there is no unified analysis for a large class of games that includes both strongly monotone and bilinear games; ii) it is not known whether the rate achieved by extragradient can be improved, e.g. by considering multiple extrapolation steps. We answer these questions through new analysis of the extragradient's local and global convergence properties. Our analysis covers the whole range of settings between purely bilinear and strongly monotone games. It reveals that extragradient converges via different mechanisms at these extremes; in between, it exploits the most favorable mechanism for the given problem. We then present lower bounds on the rate of convergence for a wide class of algorithms with any number of extrapolations. Our bounds prove that the extragradient achieves the optimal rate in this class, and that our upper bounds are tight. Our precise characterization of the extragradient's convergence behavior in games shows that, unlike in convex optimization, the extragradient method may be much faster than the gradient method.

Includes members:
  Member "on finding local nash equilibria and only local nash equilibria in zero sum games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gans may have no nash equilibria")
  Member "a closer look at the optimization landscapes of generative adversarial networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "local saddle point optimization a curvature exploitation approach":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a mean field analysis of two player zero sum games")
  Member "a variational inequality perspective on generative adversarial nets":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "last iterate is slower than averaged iterate in smooth convex concave saddle point problems")
  Member "the mechanics of n player differentiable games":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners")
  Member "the numerics of gans":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "when relation networks meet gans relation gans with triplet loss")
  Member "intrinsic motivation and automatic curricula via asymmetric self play":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "explore discover and learn unsupervised discovery of state covering skills")
  Member "improved training of wasserstein gans":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "generative adversarial networks in computer vision a survey and taxonomy")

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)