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 "a convergence analysis of nonlinearly constrained admm in deep learning"):
  Abstract: Efficient training of deep neural networks (DNNs) is a challenge due to the associated highly nonconvex optimization. The alternating direction method of multipliers (ADMM) has attracted rising attention in deep learning for its potential of distributed computing. However, it remains an open problem to establish the convergence of ADMM in DNN training due to the nonlinear constraints involved. In this paper, we provide an answer to this problem by establishing the convergence of some nonlinearly constrained ADMM for DNNs with smooth activations. To be specific, we establish the global convergence to a Karush-Kuhn-Tucker (KKT) point at a ${\cal O}(1/k)$ rate. To achieve this goal, the key development lies in a new local linear approximation technique which enables us to overcome the hurdle of nonlinear constraints in ADMM for DNNs.

Includes members:
  Member "deep component analysis via alternating direction neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "robust conditional generative adversarial networks")
  Member "fenchel lifted networks a lagrange relaxation of neural network training":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "effects of depth width and initialization a convergence analysis of layer wise training for deep linear neural networks")
  Member "alternating direction method of multipliers for sparse convolutional neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a systematic dnn weight pruning framework using alternating direction method of multipliers")
  Member "training neural networks without gradients a scalable admm approach":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "deep connections between learning from limited labels physical parameter estimation inspiration for regularization")
  Member "constructive neural network learning":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximation smooth and sparse functions by deep neural networks without saturation")
  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")

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)