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: "convexifying the bethe free energy"
  Abstract: The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.

Connected through hyperedge HE-1 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference"):
  with members:
    - "near linear time approximation algorithms for optimal transport via sinkhorn iteration"
    - "convergent message passing algorithms for inference over general graphs with convex free energies"
    - "map estimation linear programming and belief propagation with convex free energies"

Connected through hyperedge HE-2 (induced by source paper "amortized bethe free energy minimization for learning mrfs"):
  with members:
    - "a tutorial on deep latent variable models of natural language"
    - "learning approximate inference networks for structured prediction"
    - "inference in probabilistic graphical models by graph neural networks"
    - "backpropagation through the void optimizing control variates for black box gradient estimation"
    - "rebar low variance unbiased gradient estimates for discrete latent variable models"
    - "attention is all you need"
    - "neural variational inference and learning in undirected graphical models"
    - "perceptual losses for real time style transfer and super resolution"

Connected through hyperedge HE-3 (induced by source paper "graph structured prediction energy networks"):
  with members:
    - "deep structured prediction with nonlinear output transformations"
    - "learning approximate inference networks for structured prediction"
    - "deep value networks learn to evaluate and iteratively refine structured outputs"
    - "end to end sequence labeling via bi directional lstm cnns crf"
    - "neural architectures for named entity recognition"
    - "structured prediction energy networks"
    - "deeply learning the messages in message passing inference"
    - "conditional random fields as recurrent neural networks"

Connected through hyperedge HE-4 (induced by source paper "block belief propagation for parameter learning in markov random fields"):
  with members:
    - "deeply learning the messages in message passing inference"
    - "very deep convolutional networks for large scale image recognition"
    - "fully convolutional networks for semantic segmentation"
    - "learning graphical model parameters with approximate marginal inference"
    - "efficient decomposed learning for structured prediction"
    - "counting belief propagation"
    - "a new class of upper bounds on the log partition function"
    - "stochastic belief propagation a low complexity alternative to the sum product algorithm"

Connected through hyperedge HE-5 (induced by source paper "iterative receivers for downlink mimo scma message passing and distributed cooperative detection"):
  with members:
    - "wireless powered communications with non orthogonal multiple access"
    - "nonorthogonal multiple access in large scale underlay cognitive radio networks"
    - "a survey of downlink non orthogonal multiple access for 5g wireless communication networks"
    - "gaussian message passing iterative detection for mimo noma systems with massive access"
    - "fast admm algorithm for distributed optimization with adaptive penalty"
    - "scma codebook design"
    - "what will 5g be"
    - "on the performance of non orthogonal multiple access in 5g systems with randomly deployed users"

Connected through hyperedge HE-6 (induced by source paper "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"):
  with members:
    - "rounding sum of squares relaxations"
    - "a new class of upper bounds on the log partition function"
    - "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
    - "correlation decay up to uniqueness in spin systems"
    - "rounding semidefinite programming hierarchies via global correlation"
    - "approximate counting via correlation decay in spin systems"
    - "computational transition at the uniqueness threshold"
    - "complexity of combinatorial market makers"

Connected through hyperedge HE-7 (induced by source paper "message passing and combinatorial optimization"):
  with members:
    - "augmentative message passing for traveling salesman problem and graph partitioning"
    - "perturbed message passing for constraint satisfaction problems"
    - "revisiting algebra and complexity of inference in graphical models"
    - "on map inference by mwss on perfect graphs"
    - "loopy belief propagation for approximate inference an empirical study"
    - "graphical models for game theory"
    - "message passing algorithms reparameterizations and splittings"
    - "the bethe permanent of a nonnegative matrix"

Connected through hyperedge HE-8 (induced by source paper "approximating the bethe partition function"):
  with members:
    - "on map inference by mwss on perfect graphs"
    - "loopy belief propagation for approximate inference an empirical study"
    - "belief optimization for binary networks a stable alternative to loopy belief propagation"
    - "sufficient conditions for convergence of loopy belief propagation"
    - "bethe bounds and approximating the global optimum"
    - "what cannot be learned with bethe approximations"
    - "on the partition function and random maximum a posteriori perturbations"
    - "complexity of inference in graphical models"

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.AI(Artificial Intelligence)