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: "nonlinear approximation and deep relu networks"
  Abstract: This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural networks approximate functions with classical smoothness to the same accuracy as classical linear methods of approximation, e.g. approximation by polynomials or by piecewise polynomials on prescribed partitions. However, approximation by neural networks depending on n parameters is a form of nonlinear approximation and as such should be compared with other nonlinear methods such as variable knot splines or n-term approximation from dictionaries. The performance of neural networks in targeted applications such as machine learning indicate that they actually possess even greater approximation power than these traditional methods of nonlinear approximation. The main results of this article prove that this is indeed the case. This is done by exhibiting large classes of functions which can be efficiently captured by neural networks where classical nonlinear methods fall short of the task. The present article purposefully limits itself to studying the approximation of univariate functions by ReLU networks. Many generalizations to functions of several variables and other activation functions can be envisioned. However, even in this simplest of settings considered here, a theory that completely quantifies the approximation power of neural networks is still lacking.

Connected through hyperedge HE-1 (induced by source paper "hp vpinns variational physics informed neural networks with domain decomposition"):
  with members:
    - "understanding and mitigating gradient pathologies in physics informed neural networks"
    - "variational physics informed neural networks for solving partial differential equations"
    - "varnet variational neural networks for the solution of partial differential equations"
    - "function approximation by deep networks"
    - "d3m a deep domain decomposition method for partial differential equations"
    - "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks"
    - "deepxde a deep learning library for solving differential equations"
    - "robust training and initialization of deep neural networks an adaptive basis viewpoint"

Connected through hyperedge HE-2 (induced by source paper "nonparametric regression on low dimensional manifolds using deep relu networks"):
  with members:
    - "efficient approximation of deep relu networks for functions on low dimensional manifolds"
    - "efficientnet rethinking model scaling for convolutional neural networks"
    - "universality of deep convolutional neural networks"
    - "squeeze and excitation networks"
    - "recent trends in deep learning based natural language processing"
    - "the expressive power of neural networks a view from the width"
    - "deep nets for local manifold learning"
    - "deep reinforcement learning for robotic manipulation with asynchronous off policy updates"

Connected through hyperedge HE-3 (induced by source paper "deep learning via dynamical systems an approximation perspective"):
  with members:
    - "nonlinear approximation via compositions"
    - "barron spaces and the compositional function spaces for neural network models"
    - "understanding and improving transformer from a multi particle dynamic system point of view"
    - "a priori estimates of the population risk for residual networks"
    - "approximation capabilities of neural ordinary differential equations"
    - "resnets ensemble via the feynman kac formalism to improve natural and robust accuracies"
    - "dynamically unfolding recurrent restorer a moving endpoint control method for image restoration"
    - "monge amp ere flow for generative modeling"

Connected through hyperedge HE-4 (induced by source paper "a hessian based complexity measure for deep networks"):
  with members:
    - "two models of double descent for weak features"
    - "how do infinite width bounded norm networks look in function space"
    - "on exact computation with an infinitely wide neural net"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "a generalization theory of gradient descent for learning over parameterized deep relu networks"
    - "learning and generalization in overparameterized neural networks going beyond two layers"
    - "a kernel theory of modern data augmentation"
    - "stronger generalization bounds for deep nets via a compression approach"

Connected through hyperedge HE-5 (induced by source paper "efficient approximation of deep relu networks for functions on low dimensional manifolds"):
  with members:
    - "efficientnet rethinking model scaling for convolutional neural networks"
    - "on the optimization of deep networks implicit acceleration by overparameterization"
    - "recent trends in deep learning based natural language processing"
    - "the expressive power of neural networks a view from the width"
    - "error bounds for approximations with deep relu networks"
    - "understanding deep learning requires rethinking generalization"
    - "deep nets for local manifold learning"
    - "deep reinforcement learning for robotic manipulation with asynchronous off policy updates"

Connected through hyperedge HE-6 (induced by source paper "gradient dynamics of shallow univariate relu networks"):
  with members:
    - "how do infinite width bounded norm networks look in function space"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "a comparative analysis of the optimization and generalization property of two layer neural network and random feature models under gradient descent dynamics"
    - "a generalization theory of gradient descent for learning over parameterized deep relu networks"
    - "gradient descent finds global minima of deep neural networks"
    - "overparameterized nonlinear learning gradient descent takes the shortest path"
    - "neural tangent kernel convergence and generalization in neural networks"
    - "gradient descent provably optimizes over parameterized neural networks"

Connected through hyperedge HE-7 (induced by source paper "theoretical issues in deep networks approximation optimization and generalization"):
  with members:
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "non convex learning via stochastic gradient langevin dynamics a nonasymptotic analysis"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "theory of deep learning iib optimization properties of sgd"
    - "theoretical insights into the optimization landscape of over parameterized shallow neural networks"
    - "an analytical formula of population gradient for two layered relu network and its applications in convergence and critical point analysis"
    - "how to escape saddle points efficiently"
    - "theory ii landscape of the empirical risk in deep learning"

Connected through hyperedge HE-8 (induced by source paper "variational physics informed neural networks for solving partial differential equations"):
  with members:
    - "nonlinear approximation via compositions"
    - "function approximation by deep networks"
    - "locally adaptive activation functions with slope recovery term for deep and physics informed neural networks"
    - "barron spaces and the compositional function spaces for neural network models"
    - "hidden physics models machine learning of nonlinear partial differential equations"
    - "hidden fluid mechanics a navier stokes informed deep learning framework for assimilating flow visualization data"
    - "machine learning of linear differential equations using gaussian processes"
    - "deep vs shallow networks an approximation theory perspective"

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)