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 "nonlinear approximation via compositions"):
  Abstract: Abstract   Given a function dictionary    D    and an approximation budget     N  ∈  N    , nonlinear approximation seeks the linear combination of the best    N    terms        {    T    n    }     1  ≤  n  ≤  N    ⊆  D     to approximate a given function    f    with the minimum approximation error         e    L  ,  f    ≔    min     {    g    n    }   ⊆  R  ,   {    T    n    }   ⊆  D    ‖  f   (  x  )   −    ∑    n  =  1    N      g    n      T    n     (  x  )   ‖  .      Motivated by recent success of deep learning, we propose dictionaries with functions in a form of compositions, i.e.,       T   (  x  )   =    T     (  L  )     ∘    T     (  L  −  1  )     ∘  ⋯  ∘    T     (  1  )      (  x  )       for all     T  ∈  D    , and implement    T    using ReLU feed-forward neural networks (FNNs) with    L    hidden layers. We further quantify the improvement of the best    N   -term approximation rate in terms of    N    when    L    is increased from 1 to 2 or 3 to show the power of compositions. In the case when     L  >  3    , our analysis shows that increasing    L    cannot improve the approximation rate in terms of    N   .  In particular, for any function    f    on     [  0  ,  1  ]    , regardless of its smoothness and even the continuity, if    f    can be approximated using a dictionary when     L  =  1     with the best    N   -term approximation rate       e    L  ,  f    =  O   (    N    −  η    )     , we show that dictionaries with     L  =  2     can improve the best    N   -term approximation rate to       e    L  ,  f    =  O   (    N    −  2  η    )     . We also show that for Holder continuous functions of order    α    on       [  0  ,  1  ]     d     , the application of a dictionary with     L  =  3     in nonlinear approximation can achieve an essentially tight best    N   -term approximation rate       e    L  ,  f    =  O   (    N    −  2  α  ∕  d    )     . Finally, we show that dictionaries consisting of wide FNNs with a few hidden layers are more attractive in terms of computational efficiency than dictionaries with narrow and very deep FNNs for approximating Holder continuous functions if the number of computer cores is larger than    N    in parallel computing.

Includes members:
  Member "exponential convergence of the deep neural network approximation for analytic functions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "deep network approximation for smooth functions")
  Member "optimal approximation of continuous functions by very deep relu networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "neural contextual bandits with ucb based exploration")
  Member "the loss surface of deep and wide neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "translating diffusion wavelets and regularisation into residual networks")
  Member "the expressive power of neural networks a view from the width":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "sparse weight activation training")
  Member "error bounds for approximations with deep relu networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "neural contextual bandits with ucb based exploration")
  Member "adam a method for stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "nonlinear basis pursuit":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "hp vpinns variational physics informed neural networks with domain 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.LG(Machine Learning)