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 "estimation in the spiked wigner model a short proof of the replica formula"):
  Abstract: We consider the problem of estimating the rank-one perturbation of a Wigner matrix in a setting of low signal-to-noise ratio. This serves as a simple model for principal component analysis in high dimensions. The mutual information per variable between the spike and the observed matrix, or equivalently, the normalized Kullback-Leibler divergence between the planted and null models are known to converge to the so-called replica-symmetric formula, the properties of which determine the fundamental limits of estimation in this model. We provide in this note a short and transparent proof of this formula, based on simple executions of Gaussian interpolations and standard concentration-of-measure arguments. The Franz-Parisi potential, that is, the free entropy at a fixed overlap, plays an important role in our proof. Furthermore, our proof can be generalized straightforwardly to spiked tensor models of even order.

Includes members:
  Member "optimal errors and phase transitions in high dimensional generalized linear models":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "inference in multi layer networks with matrix valued unknowns")
  Member "the stochastic interpolation method a simple scheme to prove replica formulas in bayesian inference":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "entropy and mutual information in models of deep neural networks")
  Member "the layered structure of tensor estimation and its mutual information":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "optimal errors and phase transitions in high dimensional generalized linear models")
  Member "phase transitions optimal errors and optimality of message passing in generalized linear models":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "understanding phase transitions via mutual information and mmse")
  Member "mutual information in rank one matrix estimation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "overlap matrix concentration in optimal bayesian inference")
  Member "mutual information for symmetric rank one matrix estimation a proof of the replica formula":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "phase transitions in sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "a statistical model for tensor pca":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "community detection on mixture multi layer networks via regularized tensor decomposition")

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)