human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "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.

Includes members:
  Member "scaling limits of wide neural networks with weight sharing gaussian process behavior gradient independence and neural tangent kernel derivation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "quadratic suffices for over parametrization via matrix chernoff bound":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "over parameterized adversarial training an analysis overcoming the curse of dimensionality")
  Member "mean field limit of the learning dynamics of multilayer neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a rigorous framework for the mean field limit of multilayer neural networks")
  Member "on exact computation with an infinitely wide neural net":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "fine grained analysis of optimization and generalization for overparameterized two layer neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "elimination of all bad local minima in deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "on the power and limitations of random features for understanding neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "what can resnet learn efficiently going beyond kernels":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "backward feature correction how deep learning performs deep learning")

Question: Please tell me which class the source paper 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)