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: "analysis of the generalization error empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of black scholes partial differential equations"
  Abstract: The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined Deep Learning, revolutionized the area of artificial intelligence, machine learning, and data analysis. More recently, these methods have been applied to the numerical solution of high dimensional PDEs with great success. In particular, recent simulations indicate that deep learning based algorithms are capable of overcoming the curse of dimensionality for the numerical solution of linear Kolmogorov PDEs. Kolmogorov PDEs have been widely used in models from engineering, finance, and the natural sciences. Nearly all approximation methods for Kolmogorov PDEs in the literature suffer under the curse of dimensionality. By contrast, in recent work by some of the authors it was shown that deep ReLU neural networks are capable of approximating solutions of Kolmogorov PDEs without incurring the curse of dimensionality. The present paper considerably strengthens these results by providing an analysis of the generalization error. In particular we show that for Kolmogorov PDEs with affine drift and diffusion coefficients and a given accuracy $\varepsilon>0$, ERM over deep neural network hypothesis classes of size scaling polynomially in the dimension $d$ and $\varepsilon^{-1}$ and with a number of training samples scaling polynomially in the dimension $d$ and $\varepsilon^{-1}$ approximates the solution of the Kolmogorov PDE to within accuracy $\varepsilon$ with high probability. We conclude that ERM over deep neural network hypothesis classes breaks the curse of dimensionality for the numerical solution of linear Kolmogorov PDEs with affine drift and diffusion coefficients. To the best of our knowledge this is the first rigorous mathematical result that proves the efficiency of deep learning methods for high dimensional problems.

Connected through hyperedge HE-1 (induced by source paper "the gap between theory and practice in function approximation with deep neural networks"):
  with members:
    - "deep network approximation for smooth functions"
    - "the troublesome kernel why deep learning for inverse problems is typically unstable"
    - "greedy shallow networks a new approach for constructing and training neural networks"
    - "deep double descent where bigger models and more data hurt"
    - "growing axons greedy learning of neural networks with application to function approximation"
    - "a polynomial based approach for architectural design and learning with deep neural networks"
    - "on instabilities of deep learning in image reconstruction does ai come at a cost"
    - "neural network integral representations with the relu activation function"

Connected through hyperedge HE-2 (induced by source paper "on the space time expressivity of resnets"):
  with members:
    - "resnet with one neuron hidden layers is a universal approximator"
    - "stable architectures for deep neural networks"
    - "beyond finite layer neural networks bridging deep architectures and numerical differential equations"
    - "why deep neural networks for function approximation"
    - "learning functions when is deep better than shallow"
    - "understanding deep neural networks with rectified linear units"
    - "deep residual learning for image recognition"

Connected through hyperedge HE-3 (induced by source paper "how degenerate is the parametrization of neural networks with the relu activation function"):
  with members:
    - "towards a regularity theory for relu networks chain rule and global error estimates"
    - "gradient descent finds global minima of deep neural networks"
    - "darts differentiable architecture search"
    - "the universal approximation power of finite width deep relu networks"
    - "a convergence theory for deep learning via over parameterization"
    - "spectrally normalized margin bounds for neural networks"
    - "size independent sample complexity of neural networks"
    - "nearly tight vc dimension and pseudodimension bounds for piecewise linear neural networks"

Connected through hyperedge HE-4 (induced by source paper "deep neural network approximation theory"):
  with members:
    - "optimal approximation with sparsely connected deep neural networks"
    - "error bounds for approximations with deep relu networks"
    - "convolutional rectifier networks as generalized tensor decompositions"
    - "deep vs shallow networks an approximation theory perspective"
    - "why deep neural networks for function approximation"
    - "the power of depth for feedforward neural networks"
    - "representation benefits of deep feedforward networks"
    - "deep residual learning for image recognition"

Connected through hyperedge HE-5 (induced by source paper "towards a regularity theory for relu networks chain rule and global error estimates"):
  with members:
    - "deep neural network approximation theory"
    - "optimal approximation of continuous functions by very deep relu networks"
    - "the deep ritz method a deep learning based numerical algorithm for solving variational problems"

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)