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 "super resolution extremal functions and the condition number of vandermonde matrices"):
  Abstract: Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. #R##N#Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.

Includes members:
  Member "music for single snapshot spectral estimation stability and super resolution":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the stable resolution limit of total variation regularization for spike deconvolution")
  Member "smoothed analysis of tensor decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "improper learning for non stochastic control")
  Member "a polynomial time algorithm for lossy population recovery":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "efficient average case population recovery in the presence of insertions and deletions")
  Member "fourier pca and robust tensor decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "learning two layer rectified neural networks in polynomial time")
  Member "support detection in super resolution":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")
  Member "nearly optimal sparse fourier transform":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "privacy preserving learning via deep net pruning")
  Member "compressed sensing off the grid":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")
  Member "super resolution from noisy data":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "approximate support recovery of atomic line spectral estimation a tale of resolution and precision")

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)