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 convex duality framework for gans"
  Abstract: Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative model minimizing a divergence measure, e.g. the Jensen-Shannon (JS) divergence, to the data distribution. However, in practice the discriminator is constrained to be in a smaller class $\mathcal{F}$ such as neural nets. Then, a natural question is how the divergence minimization interpretation changes as we constrain $\mathcal{F}$. In this work, we address this question by developing a convex duality framework for analyzing GANs. For a convex set $\mathcal{F}$, this duality framework interprets the original GAN formulation as finding the generative model with minimum JS-divergence to the distributions penalized to match the moments of the data distribution, with the moments specified by the discriminators in $\mathcal{F}$. We show that this interpretation more generally holds for f-GAN and Wasserstein GAN. As a byproduct, we apply the duality framework to a hybrid of f-divergence and Wasserstein distance. Unlike the f-divergence, we prove that the proposed hybrid divergence changes continuously with the generative model, which suggests regularizing the discriminator's Lipschitz constant in f-GAN and vanilla GAN. We numerically evaluate the power of the suggested regularization schemes for improving GAN's training performance.

Connected through hyperedge HE-1 (induced by source paper "gans may have no nash equilibria"):
  with members:
    - "what is local optimality in nonconvex nonconcave minimax optimization"
    - "lipschitz generative adversarial nets"
    - "on gradient descent ascent for nonconvex concave minimax problems"
    - "policy optimization provably converges to nash equilibria in zero sum linear quadratic games"
    - "on finding local nash equilibria and only local nash equilibria in zero sum games"
    - "sgd learns one layer networks in wgans"
    - "on solving minimax optimization locally a follow the ridge approach"
    - "convergence of learning dynamics in stackelberg games"

Connected through hyperedge HE-2 (induced by source paper "smoothness and stability in gans"):
  with members:
    - "probability functional descent a unifying perspective on gans variational inference and reinforcement learning"
    - "beyond local nash equilibria for adversarial networks"
    - "spectral normalization for generative adversarial networks"
    - "on the convergence and robustness of training gans with regularized optimal transport"
    - "large scale gan training for high fidelity natural image synthesis"
    - "on convergence and stability of gans"
    - "which training methods for gans do actually converge"
    - "progressive growing of gans for improved quality stability and variation"

Connected through hyperedge HE-3 (induced by source paper "deconstructing generative adversarial networks"):
  with members:
    - "the optimal approximation factor in density estimation"
    - "stabilizing gan training with multiple random projections"
    - "approximability of discriminators implies diversity in gans"
    - "on the convergence and robustness of training gans with regularized optimal transport"
    - "large scale gan training for high fidelity natural image synthesis"
    - "on the implicit assumptions of gans"
    - "solving approximate wasserstein gans to stationarity"
    - "multi agent diverse generative adversarial networks"

Connected through hyperedge HE-4 (induced by source paper "bridging the gap between f gans and wasserstein gans"):
  with members:
    - "generative modeling by estimating gradients of the data distribution"
    - "learning implicit generative models with the method of learned moments"
    - "breaking the curse of horizon infinite horizon off policy estimation"
    - "spectral normalization for generative adversarial networks"
    - "large scale gan training for high fidelity natural image synthesis"
    - "the inductive bias of restricted f gans"
    - "progressive growing of gans for improved quality stability and variation"
    - "approximation and convergence properties of generative adversarial learning"

Connected through hyperedge HE-5 (induced by source paper "lipschitz generative adversarial nets"):
  with members:
    - "spectral normalization for generative adversarial networks"
    - "on convergence and stability of gans"
    - "the cramer distance as a solution to biased wasserstein gradients"
    - "which training methods for gans do actually converge"
    - "loss sensitive generative adversarial networks on lipschitz densities"
    - "progressive growing of gans for improved quality stability and variation"
    - "the numerics of gans"
    - "approximation and convergence properties of generative adversarial learning"

Connected through hyperedge HE-6 (induced by source paper "probability functional descent a unifying perspective on gans variational inference and reinforcement learning"):
  with members:
    - "policy optimization as wasserstein gradient flows"
    - "adversarial distillation of bayesian neural network posteriors"
    - "on wasserstein reinforcement learning and the fokker planck equation"
    - "sbeed convergent reinforcement learning with nonlinear function approximation"
    - "adversarial variational bayes unifying variational autoencoders and generative adversarial networks"
    - "boosting the actor with dual critic"
    - "learning from conditional distributions via dual embeddings"
    - "generative adversarial imitation learning"

Connected through hyperedge HE-7 (induced by source paper "towards efficient and unbiased implementation of lipschitz continuity in gans"):
  with members:
    - "lipschitz generative adversarial nets"
    - "on the convergence of adam and beyond"
    - "a sufficient condition for convergences of adam and rmsprop"
    - "spectral normalization for generative adversarial networks"
    - "banach wasserstein gan"
    - "on convergence and stability of gans"
    - "adashift decorrelation and convergence of adaptive learning rate methods"
    - "gans trained by a two time scale update rule converge to a nash equilibrium"

Connected through hyperedge HE-8 (induced by source paper "capacity bounded differential privacy"):
  with members:
    - "optimizing error of high dimensional statistical queries under differential privacy"
    - "the inductive bias of restricted f gans"
    - "information privacy and stability in adaptive data analysis"
    - "generalization for adaptively chosen estimators via stable median"
    - "approximation and convergence properties of generative adversarial learning"
    - "renyi differential privacy"
    - "generalization and equilibrium in generative adversarial nets gans"
    - "preserving statistical validity in adaptive data analysis"

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)