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: "optimal approximation with sparsely connected deep neural networks"
  Abstract: We derive fundamental lower bounds on the connectivity and the memory requirements of deep neural networks guaranteeing uniform approximation rates for arbitrary function classes in $L^2(\mathbb{R}^d)$. In other words, we establish a connection between the complexity of a function class and the complexity of deep neural networks approximating functions from this class to within a prescribed accuracy. Additionally, we prove that our lower bounds are achievable for a broad family of function classes. Specifically, all function classes that are optimally approximated by a general class of representation systems---so-called affine systems---can be approximated by deep neural networks with minimal connectivity and memory requirements. Affine systems encompass a wealth of representation systems from applied harmonic analysis such as wavelets, ridgelets, curvelets, shearlets, $\alpha$-shearlets, and more generally $\alpha$-molecules. Our central result elucidates a remarkable universality property of neural networks and shows that they achieve the optimum approximation properties of all affine systems combined. As a specific example, we consider the class of $\alpha^{-1}$-cartoon-like functions, which is approximated optimally by $\alpha$-shearlets. We also explain how our results can be extended to the case of functions on low-dimensional immersed manifolds. Finally, we present numerical experiments demonstrating that the standard stochastic gradient descent algorithm generates deep neural networks providing close-to-optimal approximation rates at minimal connectivity. Moreover, these results indicate that stochastic gradient descent can actually learn approximations that are sparse in the representation systems optimally sparsifying the function class the network is trained on.

Connected through hyperedge HE-1 (induced by source paper "deep network approximation for smooth functions"):
  with members:
    - "nonlinear approximation via compositions"
    - "exponential convergence of the deep neural network approximation for analytic functions"
    - "construction of neural networks for realization of localized deep learning"
    - "universality of deep convolutional neural networks"
    - "optimal approximation of continuous functions by very deep relu networks"
    - "the expressive power of neural networks a view from the width"
    - "error bounds for approximations with deep relu networks"

Connected through hyperedge HE-2 (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"
    - "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"
    - "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"

Connected through hyperedge HE-3 (induced by source paper "deep neural network approximation theory"):
  with members:
    - "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"
    - "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-4 (induced by source paper "data driven approximation of parametrized pdes by reduced basis and neural networks"):
  with members:
    - "model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders"
    - "a comprehensive analysis of deep regression"
    - "physics informed deep learning part ii data driven discovery of nonlinear partial differential equations"
    - "recent trends in deep learning based natural language processing"
    - "residual attention network for image classification"
    - "adam a method for stochastic optimization"
    - "convolutional neural networks for sentence classification"
    - "natural language processing almost from scratch"

Connected through hyperedge HE-5 (induced by source paper "on the power of over parametrization in neural networks with quadratic activation"):
  with members:
    - "generalization error bounds for noisy iterative algorithms"
    - "learning one hidden layer neural networks with landscape design"
    - "beating the perils of non convexity guaranteed training of neural networks using tensor methods"
    - "gradient descent learns one hidden layer cnn don t be afraid of spurious local minima"
    - "fisher rao metric geometry and complexity of neural networks"
    - "generalization bounds of sgld for non convex learning two theoretical viewpoints"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "computing nonvacuous generalization bounds for deep stochastic neural networks with many more parameters than training data"

Connected through hyperedge HE-6 (induced by source paper "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"):
  with members:
    - "how degenerate is the parametrization of neural networks with the relu activation function"
    - "gradient descent finds global minima of deep neural networks"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "universal approximations of invariant maps by neural networks"
    - "the universal approximation power of finite width deep relu networks"
    - "stronger generalization bounds for deep nets via a compression approach"
    - "a convergence theory for deep learning via over parameterization"
    - "exploring generalization in deep learning"

Connected through hyperedge HE-7 (induced by source paper "universality of deep convolutional neural networks"):
  with members:
    - "error bounds for approximations with deep relu networks"
    - "deep vs shallow networks an approximation theory perspective"
    - "benefits of depth in neural networks"
    - "distributed learning with regularized least squares"
    - "the power of depth for feedforward neural networks"
    - "consistency analysis of an empirical minimum error entropy algorithm"
    - "invariant scattering convolution networks"

Connected through hyperedge HE-8 (induced by source paper "the universal approximation power of finite width deep relu networks"):
  with members:
    - "on the universal approximability and complexity bounds of quantized relu neural networks"
    - "error bounds for approximations with deep relu networks"
    - "why deep neural networks for function approximation"
    - "representation benefits of deep feedforward networks"

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)