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 "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"):
  Abstract: The free energy is a key quantity of interest in Ising models, but unfortunately, computing it in general is computationally intractable. Two popular (variational) approximation schemes for estimating the free energy of general Ising models (in particular, even in regimes where correlation decay does not hold) are: (i) the mean-field approximation with roots in statistical physics, which estimates the free energy from below, and (ii) hierarchies of convex relaxations with roots in theoretical computer science, which estimate the free energy from above. We show, surprisingly, that the tight regime for both methods to compute the free energy to leading order is identical. #R##N#More precisely, we show that the mean-field approximation is within $O((n\|J\|_{F})^{2/3})$ of the free energy, where $\|J\|_F$ denotes the Frobenius norm of the interaction matrix of the Ising model. This simultaneously subsumes both the breakthrough work of Basak and Mukherjee, who showed the tight result that the mean-field approximation is within $o(n)$ whenever $\|J\|_{F} = o(\sqrt{n})$, as well as the work of Jain, Koehler, and Mossel, who gave the previously best known non-asymptotic bound of $O((n\|J\|_{F})^{2/3}\log^{1/3}(n\|J\|_{F}))$. We give a simple, algorithmic proof of this result using a convex relaxation proposed by Risteski based on the Sherali-Adams hierarchy, automatically giving sub-exponential time approximation schemes for the free energy in this entire regime. Our algorithmic result is tight under Gap-ETH. #R##N#We furthermore combine our techniques with spin glass theory to prove (in a strong sense) the optimality of correlation rounding, refuting a recent conjecture of Allen, O'Donnell, and Zhou. Finally, we give the tight generalization of all of these results to $k$-MRFs, capturing as a special case previous work on approximating MAX-$k$-CSP.

Includes members:
  Member "the vertex sample complexity of free energy is polynomial":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the mean field approximation information inequalities algorithms and complexity")
  Member "the mean field approximation information inequalities algorithms and complexity":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "spectral approximate inference")
  Member "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "a birthday repetition theorem and complexity of approximating dense csps":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "parameterized inapproximability for steiner orientation by gap amplification")
  Member "sub exponential approximation schemes for csps from dense to almost sparse":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sublinear algorithms for maxcut and correlation clustering")
  Member "conditioning and covariance on caterpillars":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "information theoretic thresholds from the cavity method")
  Member "rounding semidefinite programming hierarchies via global correlation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "approximating csps with global cardinality constraints using sdp hierarchies":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "new dependencies of hierarchies in polynomial optimization")

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)