human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "piecewise convexity of artificial neural networks"
  Abstract: Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. Firstly, that the network is piecewise convex as a function of the input data. Secondly, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Finally, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space.

Connected through hyperedge HE-1 (induced by source paper "when can neural networks learn connected decision regions"):
  with members:
    - "beating the perils of non convexity guaranteed training of neural networks using tensor methods"
    - "learning relus via gradient descent"
    - "optimization landscape and expressivity of deep cnns"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "the loss surface of deep and wide neural networks"
    - "the expressive power of neural networks a view from the width"
    - "theory ii landscape of the empirical risk in deep learning"
    - "error bounds for approximations with deep relu networks"

Connected through hyperedge HE-2 (induced by source paper "the loss surface of deep and wide neural networks"):
  with members:
    - "beating the perils of non convexity guaranteed training of neural networks using tensor methods"
    - "eigenvalues of the hessian in deep learning singularity and beyond"
    - "learning relus via gradient descent"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "theory ii landscape of the empirical risk in deep learning"
    - "understanding deep learning requires rethinking generalization"
    - "globally optimal training of generalized polynomial neural networks with nonlinear spectral methods"
    - "how far can we go without convolution improving fully connected networks"

Connected through hyperedge HE-3 (induced by source paper "exploiting layerwise convexity of rectifier networks with sign constrained weights"):
  with members:
    - "densely connected convolutional networks"
    - "matrix completion has no spurious local minimum"
    - "on the computational efficiency of training neural networks"
    - "deep learning face representation by joint identification verification"
    - "visualizing and understanding convolutional networks"
    - "multi column deep neural networks for image classification"

Question: Please tell me which class the center node 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)