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: "global convergence to the equilibrium of gans using variational inequalities"
  Abstract: In optimization, the negative gradient of a function denotes the direction of steepest descent. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. In this work, we show that these orthogonal directions that are ignored by gradient descent can be critical in equilibrium problems. Equilibrium problems have drawn heightened attention in machine learning due to the emergence of the Generative Adversarial Network (GAN). We use the framework of Variational Inequalities to analyze popular training algorithms for a fundamental GAN variant: the Wasserstein Linear-Quadratic GAN. We show that the steepest descent direction causes divergence from the equilibrium, and convergence to the equilibrium is achieved through following a particular orthogonal direction. We call this successful technique Crossing-the-Curl, named for its mathematical derivation as well as its intuition: identify the game's axis of rotation and move "across" space in the direction towards smaller "curling".

Connected through hyperedge HE-1 (induced by source paper "smooth markets a basic mechanism for organizing gradient based learners"):
  with members:
    - "logan latent optimisation for generative adversarial networks"
    - "finite regret and cycles with fixed step size via alternating gradient descent ascent"
    - "a closer look at the optimization landscapes of generative adversarial networks"
    - "differentiable game mechanics"
    - "the mechanics of n player differentiable games"
    - "the numerics of gans"
    - "multiplicative weights update with constant step size in congestion games convergence limit cycles and chaos"
    - "unpaired image to image translation using cycle consistent adversarial networks"

Connected through hyperedge HE-2 (induced by source paper "implicit competitive regularization in gans"):
  with members:
    - "coherent gradients an approach to understanding generalization in gradient descent based optimization"
    - "what is local optimality in nonconvex nonconcave minimax optimization"
    - "on finding local nash equilibria and only local nash equilibria in zero sum games"
    - "a gradual semi discrete approach to generative network training via explicit wasserstein minimization"
    - "stochastic mirror descent on overparameterized nonlinear models convergence implicit regularization and generalization"
    - "a closer look at the optimization landscapes of generative adversarial networks"
    - "implicit regularization in deep matrix factorization"
    - "implicit regularization in over parameterized neural networks"

Connected through hyperedge HE-3 (induced by source paper "logan latent optimisation for generative adversarial networks"):
  with members:
    - "deep compressed sensing"
    - "adversarial video generation on complex datasets"
    - "differentiable game mechanics"
    - "cgans with projection discriminator"
    - "the mechanics of n player differentiable games"
    - "spectral normalization for generative adversarial networks"
    - "large scale gan training for high fidelity natural image synthesis"
    - "adversarial audio synthesis"

Connected through hyperedge HE-4 (induced by source paper "differentiable game mechanics"):
  with members:
    - "a variational inequality perspective on generative adversarial nets"
    - "re evaluating evaluation"
    - "negative momentum for improved game dynamics"
    - "which training methods for gans do actually converge"
    - "gans trained by a two time scale update rule converge to a nash equilibrium"
    - "strongly typed agents are guaranteed to interact safely"
    - "learning with opponent learning awareness"
    - "feudal networks for hierarchical reinforcement learning"

Connected through hyperedge HE-5 (induced by source paper "on solving minimax optimization locally a follow the ridge approach"):
  with members:
    - "what is local optimality in nonconvex nonconcave minimax optimization"
    - "on gradient descent ascent for nonconvex concave minimax problems"
    - "on finding local nash equilibria and only local nash equilibria in zero sum games"
    - "a closer look at the optimization landscapes of generative adversarial networks"
    - "convergence of learning dynamics in stackelberg games"
    - "local saddle point optimization a curvature exploitation approach"
    - "the mechanics of n player differentiable games"
    - "optimistic mirror descent in saddle point problems going the extra gradient mile"

Connected through hyperedge HE-6 (induced by source paper "ode analysis of stochastic gradient methods with optimism and anchoring for minimax problems and gans"):
  with members:
    - "training gans with centripetal acceleration"
    - "improving the improved training of wasserstein gans a consistency term and its dual effect"
    - "a variational inequality perspective on generative adversarial nets"
    - "optimistic mirror descent in saddle point problems going the extra gradient mile"
    - "spectral normalization for generative adversarial networks"
    - "which training methods for gans do actually converge"
    - "the numerics of gans"
    - "stabilizing training of generative adversarial networks through regularization"

Connected through hyperedge HE-7 (induced by source paper "stein bridging enabling mutual reinforcement between explicit and implicit generative models"):
  with members:
    - "implicit generation and generalization in energy based models"
    - "a variational inequality perspective on generative adversarial nets"
    - "learning implicit generative models by teaching explicit ones"
    - "large scale gan training for high fidelity natural image synthesis"
    - "calibrating energy based generative adversarial networks"
    - "stabilizing training of generative adversarial networks through regularization"
    - "improved training of wasserstein gans"
    - "wasserstein distributional robustness and regularization in statistical learning"

Connected through hyperedge HE-8 (induced by source paper "lrs dag low resource supervised domain adaptation with generalization across domains"):
  with members:
    - "nam non adversarial unsupervised domain mapping"
    - "cycada cycle consistent adversarial domain adaptation"
    - "few shot adversarial domain adaptation"
    - "the numerics of gans"
    - "unified deep supervised domain adaptation and generalization"
    - "unsupervised image to image translation networks"
    - "unpaired image to image translation using cycle consistent adversarial networks"
    - "associative domain adaptation"

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)