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: "gradient descent maximizes the margin of homogeneous neural networks"
  Abstract: In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study the gradient descent or gradient flow (i.e., gradient descent with infinitesimal step size) optimizing the logistic loss or cross-entropy loss of any homogeneous model (possibly non-smooth), and show that if the training loss decreases below a certain threshold, then we can define a smoothed version of the normalized margin which increases over time. We also formulate a natural constrained optimization problem related to margin maximization, and prove that both the normalized margin and its smoothed version converge to the objective value at a KKT point of the optimization problem. Our results generalize the previous results for logistic regression with one-layer or multi-layer linear networks, and provide more quantitative convergence results with weaker assumptions than previous results for homogeneous smooth neural networks. We conduct several experiments to justify our theoretical finding on MNIST and CIFAR-10 datasets. Finally, as margin is closely related to robustness, we discuss potential benefits of training longer for improving the robustness of the model.

Connected through hyperedge HE-1 (induced by source paper "mean field analysis of two layer neural networks non asymptotic rates and generalization bounds"):
  with members:
    - "backward feature correction how deep learning performs deep learning"
    - "how much over parameterization is sufficient to learn deep relu networks"
    - "beyond linearization on quadratic and higher order approximation of wide neural networks"
    - "towards understanding the spectral bias of deep learning"
    - "an improved analysis of training over parameterized deep neural networks"
    - "generalization error bounds of gradient descent for learning over parameterized deep relu networks"
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "over parameterized two level neural networks can learn near optimal feature representations"

Connected through hyperedge HE-2 (induced by source paper "unique properties of wide minima in deep networks"):
  with members:
    - "a tail index analysis of stochastic gradient noise in deep neural networks"
    - "implicit regularization of normalization methods"
    - "on the optimization of deep networks implicit acceleration by overparameterization"
    - "implicit bias of gradient descent on linear convolutional networks"
    - "gradient descent aligns the layers of deep linear networks"
    - "step size matters in deep learning"
    - "algorithmic regularization in learning deep homogeneous models layers are automatically balanced"
    - "three factors influencing minima in sgd"

Connected through hyperedge HE-3 (induced by source paper "maximizing the total reward via reward tweaking"):
  with members:
    - "learning to generalize from sparse and underspecified rewards"
    - "extrapolating beyond suboptimal demonstrations via inverse reinforcement learning from observations"
    - "on first order meta learning algorithms"
    - "simple random search provides a competitive approach to reinforcement learning"
    - "on learning intrinsic rewards for policy gradient methods"
    - "addressing function approximation error in actor critic methods"
    - "soft actor critic off policy maximum entropy deep reinforcement learning with a stochastic actor"
    - "curiosity driven exploration by self supervised prediction"

Connected through hyperedge HE-4 (induced by source paper "how much over parameterization is sufficient to learn deep relu networks"):
  with members:
    - "two models of double descent for weak features"
    - "beyond linearization on quadratic and higher order approximation of wide neural networks"
    - "an improved analysis of training over parameterized deep neural networks"
    - "generalization error bounds of gradient descent for learning over parameterized deep relu networks"
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "over parameterized two level neural networks can learn near optimal feature representations"
    - "convex formulation of overparameterized deep neural networks"
    - "polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow relu networks"

Connected through hyperedge HE-5 (induced by source paper "theory iii dynamics and generalization in deep networks a simple solution"):
  with members:
    - "mean field limit of the learning dynamics of multilayer neural networks"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "loss landscapes of regularized linear autoencoders"
    - "learning and generalization in overparameterized neural networks going beyond two layers"
    - "gradient descent finds global minima of deep neural networks"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "algorithmic regularization in learning deep homogeneous models layers are automatically balanced"
    - "gradient descent provably optimizes over parameterized neural networks"

Connected through hyperedge HE-6 (induced by source paper "improved sample complexities for deep networks and robust classification via an all layer margin"):
  with members:
    - "a hessian based complexity measure for deep networks"
    - "learning imbalanced datasets with label distribution aware margin loss"
    - "vc classes are adversarially robustly learnable but only improperly"
    - "deterministic pac bayesian generalization bounds for deep networks via generalizing noise resilience"
    - "theoretically principled trade off between robustness and accuracy"
    - "adversarial training can hurt generalization"
    - "data dependent sample complexity of deep neural networks via lipschitz augmentation"
    - "implicit bias of gradient descent on linear convolutional networks"

Connected through hyperedge HE-7 (induced by source paper "a bayes optimal view on adversarial examples"):
  with members:
    - "adversarial examples are a natural consequence of test error in noise"
    - "theoretically principled trade off between robustness and accuracy"
    - "a simple explanation for the existence of adversarial examples with small hamming distance"
    - "on evaluating adversarial robustness"
    - "on gans and gmms"
    - "towards the first adversarially robust neural network model on mnist"
    - "adversarially robust generalization requires more data"
    - "improved training of wasserstein gans"

Connected through hyperedge HE-8 (induced by source paper "a function space view of bounded norm infinite width relu nets the multivariate case"):
  with members:
    - "two models of double descent for weak features"
    - "approximation power of random neural networks"
    - "how do infinite width bounded norm networks look in function space"
    - "neural tangent kernels transportation mappings and universal approximation"
    - "neural network with unbounded activation functions is universal approximator"
    - "error bounds for approximations with deep relu networks"
    - "understanding deep learning requires rethinking generalization"
    - "why deep neural networks for function approximation"

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)