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 "on exact and infty r enyi common informations"):
  Abstract: Recently, two extensions of Wyner's common information\textemdash exact and R\'enyi common informations\textemdash were introduced respectively by Kumar, Li, and El Gamal (KLE), and the present authors. The class of common information problems involves determining the minimum rate of the common input to two independent processors needed to exactly or approximately generate a target joint distribution. For the exact common information problem, exact generation of the target distribution is required, while for Wyner's and $\alpha$-R\'enyi common informations, the relative entropy and R\'enyi divergence with order $\alpha$ were respectively used to quantify the discrepancy between the synthesized and target distributions. The exact common information is larger than or equal to Wyner's common information. However, it was hitherto unknown whether the former is strictly larger than the latter for some joint distributions. In this paper, we first establish the equivalence between the exact and $\infty$-R\'enyi common informations, and then provide single-letter upper and lower bounds for these two quantities. For doubly symmetric binary sources, we show that the upper and lower bounds coincide, which implies that for such sources, the exact and $\infty$-R\'enyi common informations are completely characterized. Interestingly, we observe that for such sources, these two common informations are strictly larger than Wyner's. This answers an open problem posed by KLE. Furthermore, we extend Wyner's, $\infty$-R\'enyi, and exact common informations to sources with countably infinite or continuous alphabets, including Gaussian sources.

Includes members:
  Member "corrections to wyner s common information under r enyi divergence measures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "r enyi resolvability and its applications to the wiretap channel")
  Member "exact channel synthesis":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "communication for generating correlation a unifying survey")
  Member "strong functional representation lemma and applications to coding theorems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "communication for generating correlation a unifying survey")
  Member "distributed simulation of continuous random variables":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "constrained functional value under general convexity conditions with applications to distributed simulation")
  Member "generalized common information common information extraction and private sources synthesis":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "exact channel synthesis")
  Member "exact common information":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "communication for generating correlation a unifying survey")
  Member "a generalized typicality for abstract alphabets":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the renyi capacity and center")
  Member "renyi divergence and kullback leibler divergence":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "review analyze and design a comprehensive deep reinforcement learning framework")

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)