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: "dynamics of deep neural networks and neural tangent hierarchy"
  Abstract: The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in some other recent papers [6,13,14]. In the overparametrization regime, a fully-trained deep neural network is indeed equivalent to the kernel regression predictor using the limiting NTK. And the gradient descent achieves zero training loss for a deep overparameterized neural network. However, it was observed in [5] that there is a performance gap between the kernel regression using the limiting NTK and the deep neural networks. This performance gap is likely to originate from the change of the NTK along training due to the finite width effect. The change of the NTK along the training is central to describe the generalization features of deep neural networks. #R##N#In the current paper, we study the dynamic of the NTK for finite width deep fully-connected neural networks. We derive an infinite hierarchy of ordinary differential equations, the neural tangent hierarchy (NTH) which captures the gradient descent dynamic of the deep neural network. Moreover, under certain conditions on the neural network width and the data set dimension, we prove that the truncated hierarchy of NTH approximates the dynamic of the NTK up to arbitrary precision. This description makes it possible to directly study the change of the NTK for deep neural networks, and sheds light on the observation that deep neural networks outperform kernel regressions using the corresponding limiting NTK.

Connected through hyperedge HE-1 (induced by source paper "backward feature correction how deep learning performs deep learning"):
  with members:
    - "scaling limits of wide neural networks with weight sharing gaussian process behavior gradient independence and neural tangent kernel derivation"
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "width provably matters in optimization for deep linear neural networks"
    - "finite depth and width corrections to the neural tangent kernel"
    - "towards explaining the regularization effect of initial large learning rate in training neural networks"
    - "on exact computation with an infinitely wide neural net"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "can sgd learn recurrent neural networks with provable generalization"

Connected through hyperedge HE-2 (induced by source paper "frequency bias in neural networks for input of non uniform density"):
  with members:
    - "towards understanding the spectral bias of deep learning"
    - "kernel and deep regimes in overparametrized models"
    - "frequency principle fourier analysis sheds light on deep neural networks"
    - "on exact computation with an infinitely wide neural net"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "on the convergence rate of training recurrent neural networks"
    - "gradient descent provably optimizes over parameterized neural networks"
    - "eigenvalue decay implies polynomial time learnability for neural networks"

Connected through hyperedge HE-3 (induced by source paper "disentangling trainability and generalization in deep learning"):
  with members:
    - "freeze and chaos for dnns an ntk view of batch normalization checkerboard and boundary effects"
    - "scaling limits of wide neural networks with weight sharing gaussian process behavior gradient independence and neural tangent kernel derivation"
    - "a mean field theory of batch normalization"
    - "finite depth and width corrections to the neural tangent kernel"
    - "dynamical isometry and a mean field theory of lstms and grus"
    - "on exact computation with an infinitely wide neural net"
    - "transfusion understanding transfer learning for medical imaging"
    - "gradient descent finds global minima of deep neural networks"

Connected through hyperedge HE-4 (induced by source paper "asymptotics of wide networks from feynman diagrams"):
  with members:
    - "scaling limits of wide neural networks with weight sharing gaussian process behavior gradient independence and neural tangent kernel derivation"
    - "disentangling feature and lazy learning in deep neural networks an empirical study"
    - "measurements of three level hierarchical structure in the outliers in the spectrum of deepnet hessians"
    - "an investigation into neural net optimization via hessian eigenvalue density"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "gradient descent finds global minima of deep neural networks"
    - "neural tangent kernel convergence and generalization in neural networks"
    - "gradient descent happens in a tiny subspace"

Connected through hyperedge HE-5 (induced by source paper "the asymptotic spectrum of the hessian of dnn throughout training"):
  with members:
    - "freeze and chaos for dnns an ntk view of batch normalization checkerboard and boundary effects"
    - "measurements of three level hierarchical structure in the outliers in the spectrum of deepnet hessians"
    - "an investigation into neural net optimization via hessian eigenvalue density"
    - "on exact computation with an infinitely wide neural net"
    - "gradient descent happens in a tiny subspace"
    - "a convergence theory for deep learning via over parameterization"
    - "towards understanding generalization of deep learning perspective of loss landscapes"
    - "empirical analysis of the hessian of over parametrized neural networks"

Connected through hyperedge HE-6 (induced by source paper "neural spectrum alignment"):
  with members:
    - "generalization guarantees for neural networks via harnessing the low rank structure of the jacobian"
    - "kernel and deep regimes in overparametrized models"
    - "asymptotics of wide networks from feynman diagrams"
    - "gradient dynamics of shallow univariate relu networks"
    - "the convergence rate of neural networks for learned functions of different frequencies"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "general probabilistic surface optimization and log density estimation"
    - "neural tangent kernel convergence and generalization in neural 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)