human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "last iterate is slower than averaged iterate in smooth convex concave saddle point problems"):
  with members:
    - "accelerating smooth games by manipulating spectral shapes"
    - "training gans with centripetal acceleration"
    - "lower bounds and conditioning of differentiable games"
    - "finite regret and cycles with fixed step size via alternating gradient descent ascent"
    - "a variational inequality perspective on generative adversarial nets"
    - "optimistic mirror descent in saddle point problems going the extra gradient mile"
    - "negative momentum for improved game dynamics"
    - "the numerics of gans"

Connected through hyperedge HE-2 (induced by source paper "accelerating smooth games by manipulating spectral shapes"):
  with members:
    - "differentiable game mechanics"
    - "a variational inequality perspective on generative adversarial nets"
    - "the mechanics of n player differentiable games"
    - "the numerics of gans"
    - "training gans with optimism"
    - "stochastic variance reduction methods for saddle point problems"

Question: Please tell me which class the center node 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)