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 "message passing algorithms for synchronization problems over compact groups"):
  Abstract: Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3). The goal of such problems is to estimate an unknown vector of group elements given noisy relative observations. We present an efficient iterative algorithm to solve a large class of these problems, allowing for any compact group, with measurements on multiple 'frequency channels' (Fourier modes, or more generally, irreducible representations of the group). Our algorithm is a highly efficient iterative method following the blueprint of approximate message passing (AMP), which has recently arisen as a central technique for inference problems such as structured low-rank estimation and compressed sensing. We augment the standard ideas of AMP with ideas from representation theory so that the algorithm can work with distributions over compact groups. Using standard but non-rigorous methods from statistical physics we analyze the behavior of our algorithm on a Gaussian noise model, identifying phases where the problem is easy, (computationally) hard, and (statistically) impossible. In particular, such evidence predicts that our algorithm is information-theoretically optimal in many cases, and that the remaining cases show evidence of statistical-to-computational gaps.

Includes members:
  Member "finite sample analysis of approximate message passing algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "the projected power method an efficient algorithm for joint alignment from pairwise differences":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "optimal learning of joint alignments with a faulty oracle")
  Member "mutual information in rank one matrix estimation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (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-5 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "non unique games over compact groups and orientation estimation in cryo em":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "single particle cryo electron microscopy mathematical theory computational challenges and opportunities")
  Member "mmse of probabilistic low rank matrix estimation universality with respect to the output channel":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")
  Member "semidefinite programs on sparse random graphs and their application to community detection":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "computational hardness of certifying bounds on constrained pca problems")

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)