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 "generalization guarantees for neural networks via harnessing the low rank structure of the jacobian"):
  Abstract: Modern neural network architectures often generalize well despite containing many more parameters than the size of the training dataset. This paper explores the generalization capabilities of neural networks trained via gradient descent. We develop a data-dependent optimization and generalization theory which leverages the low-rank structure of the Jacobian matrix associated with the network. Our results help demystify why training and generalization is easier on clean and structured datasets and harder on noisy and unstructured datasets as well as how the network size affects the evolution of the train and test errors during training. Specifically, we use a control knob to split the Jacobian spectum into "information" and "nuisance" spaces associated with the large and small singular values. We show that over the information space learning is fast and one can quickly train a model with zero training loss that can also generalize well. Over the nuisance space training is slower and early stopping can help with generalization at the expense of some bias. We also show that the overall generalization capability of the network is controlled by how well the label vector is aligned with the information space. A key feature of our results is that even constant width neural nets can provably generalize for sufficiently nice datasets. We conduct various numerical experiments on deep networks that corroborate our theoretical findings and demonstrate that: (i) the Jacobian of typical neural networks exhibit low-rank structure with a few large singular values and many small ones leading to a low-dimensional information space, (ii) over the information space learning is fast and most of the label vector falls on this space, and (iii) label noise falls on the nuisance space and impedes optimization/generalization.

Includes members:
  Member "two models of double descent for weak features":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "size free generalization bounds for convolutional neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "towards moderate overparameterization global convergence guarantees for training shallow neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "deterministic pac bayesian generalization bounds for deep networks via generalizing noise resilience":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "training over parameterized deep resnet is almost as easy as training a two layer network":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the global convergence of training deep linear resnets")
  Member "gradient descent with early stopping is provably robust to label noise for overparameterized neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "identifying mislabeled data using the area under the margin ranking")
  Member "fine grained analysis of optimization and generalization for overparameterized two layer neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "on the power and limitations of random features for understanding neural networks":
    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)