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 "counting in graph covers a combinatorial characterization of the bethe entropy function"):
  Abstract: We present a combinatorial characterization of the Bethe entropy function of a factor graph, such a characterization being in contrast to the original, analytical, definition of this function. We achieve this combinatorial characterization by counting valid configurations in finite graph covers of the factor graph. Analogously, we give a combinatorial characterization of the Bethe partition function, whose original definition was also of an analytical nature. As we point out, our approach has similarities to the replica method, but also stark differences. The above findings are a natural backdrop for introducing a decoder for graph-based codes that we will call symbolwise graph-cover decoding, a decoder that extends our earlier work on blockwise graph-cover decoding. Both graph-cover decoders are theoretical tools that help toward a better understanding of message-passing iterative decoding, namely blockwise graph-cover decoding links max-product (min-sum) algorithm decoding with linear programming decoding, and symbolwise graph-cover decoding links sum-product algorithm decoding with Bethe free energy function minimization at temperature one. In contrast to the Gibbs entropy function, which is a concave function, the Bethe entropy function is in general not concave everywhere. In particular, we show that every code picked from an ensemble of regular low-density parity-check codes with minimum Hamming distance growing (with high probability) linearly with the block length has a Bethe entropy function that is convex in certain regions of its domain.

Includes members:
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "beyond log supermodularity lower bounds and the bethe partition function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lifted hybrid variational inference")
  Member "new generalizations of the bethe approximation via asymptotic expansion":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "loop calculus for non binary alphabets using concepts from information geometry")
  Member "central approximation in statistical physics and information theory":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new generalizations of the bethe approximation via asymptotic expansion")
  Member "the bethe partition function of log supermodular graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "lifted hybrid variational inference")
  Member "pseudocodewords from bethe permanents":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the bethe permanent of a nonnegative matrix")
  Member "connection between annealed free energy and belief propagation on random factor graph ensembles":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "threshold saturation for spatially coupled ldpc and ldgm codes on bms channels")
  Member "normal factor graphs and holographic transformations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "codes on graphs models for elementary algebraic topology and statistical physics")

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.IT(Information Theory)