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 "the geometry of sign gradient descent"):
  Abstract: Sign-based optimization methods have become popular in machine learning due to their favorable communication cost in distributed optimization and their surprisingly good performance in neural network training. Furthermore, they are closely connected to so-called adaptive gradient methods like Adam. Recent works on signSGD have used a non-standard "separable smoothness" assumption, whereas some older works study sign gradient descent as steepest descent with respect to the $\ell_\infty$-norm. In this work, we unify these existing results by showing a close connection between separable smoothness and $\ell_\infty$-smoothness and argue that the latter is the weaker and more natural assumption. We then proceed to study the smoothness constant with respect to the $\ell_\infty$-norm and thereby isolate geometric properties of the objective function which affect the performance of sign-based methods. In short, we find sign-based methods to be preferable over gradient descent if (i) the Hessian is to some degree concentrated on its diagonal, and (ii) its maximal eigenvalue is much larger than the average eigenvalue. Both properties are common in deep networks.

Includes members:
  Member "hessian based analysis of sgd for deep nets dynamics and generalization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "dissecting non vacuous generalization bounds based on the mean field approximation")
  Member "stochastic gradient methods with layer wise adaptive moments for training of deep networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "an investigation into neural net optimization via hessian eigenvalue density":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "scaling laws for neural language models")
  Member "ellipsoidal trust region methods and the marginal value of hessian information for neural network training":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on empirical comparisons of optimizers for deep learning")
  Member "signsgd with majority vote is communication efficient and fault tolerant":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "threats to federated learning a survey")
  Member "block normalized gradient method an empirical study for training deep neural network":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "automl zero evolving machine learning algorithms from scratch")
  Member "the full spectrum of deep net hessians at scale dynamics with sample size":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "scaling laws for neural language models")
  Member "dissecting adam the sign magnitude and variance of stochastic gradients":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "laprop a better way to combine momentum with adaptive gradient")

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)