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 "the bethe free energy allows to compute the conditional entropy of graphical code instances a proof from the polymer expansion"):
  Abstract: The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a low-density parity-check code used over a binary symmetric channel in a large noise regime is, with high probability, asymptotically exact as the block length grows. To arrive at this result we develop new techniques for rather general graphical models based on the loop sum as a starting point and the polymer expansion from statistical mechanics. The true free energy is computed as a series expansion containing the Bethe free energy as its zero-th order term plus a series of corrections. It is easily seen that convergence criteria for such expansions are satisfied for general high-temperature models. We apply these general results to ensembles of low-density generator-matrix and parity-check codes. While the application to generator-matrix codes follows standard "high temperature" methods, the case of parity-check codes requires non-trivial new ideas because the hard constraints correspond to a zero-temperature regime. Nevertheless one can combine the polymer expansion with expander and counting arguments to show that the difference between the true and Bethe free energies vanishes with high probability in the large block

Includes members:
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "beyond the bethe free energy of ldpc codes via polymer expansions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "concentration to zero bit error probability for regular ldpc codes on the binary symmetric channel proof by loop calculus")
  Member "the bethe partition function of log supermodular graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lifted hybrid variational inference")
  Member "partition functions of normal factor graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "codes on graphs models for elementary algebraic topology and statistical physics")
  Member "decay of correlations for sparse graph error correcting codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a scaling law to predict the finite length performance of spatially coupled ldpc codes")
  Member "sharp bounds for optimal decoding of low density parity check codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "overlap matrix concentration in optimal bayesian inference")
  Member "sufficient conditions for convergence of the sum product algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "factorized graph representations for semi supervised learning from sparse data")
  Member "loop calculus and belief propagation for q ary alphabet loop tower":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")

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)