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 "hessian based analysis of sgd for deep nets dynamics and generalization"):
  Abstract: While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new empirical observations and theoretical results on both the optimization dynamics and generalization behavior of SGD for deep nets based on the Hessian of the training loss and associated quantities. We consider three specific research questions: (1) what is the relationship between the Hessian of the loss and the second moment of stochastic gradients (SGs)? (2) how can we characterize the stochastic optimization dynamics of SGD with fixed and adaptive step sizes and diagonal pre-conditioning based on the first and second moments of SGs? and (3) how can we characterize a scale-invariant generalization bound of deep nets based on the Hessian of the loss, which by itself is not scale invariant? We shed light on these three questions using theoretical results supported by extensive empirical observations, with experiments on synthetic data, MNIST, and CIFAR-10, with different batch sizes, and with different difficulty levels by synthetically adding random labels.

Includes members:
  Member "escaping saddle points with adaptive gradient methods":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "measurements of three level hierarchical structure in the outliers in the spectrum of deepnet hessians":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the break even point on optimization trajectories of deep neural networks")
  Member "deterministic pac bayesian generalization bounds for deep networks via generalizing noise resilience":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "an investigation into neural net optimization via hessian eigenvalue density":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "scaling laws for neural language models")
  Member "on the convergence of adam and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "positively scale invariant flatness of relu neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "barcodes as summary of objective function s topology")
  Member "on the optimization of deep networks implicit acceleration by overparameterization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "small nonlinearities in activation functions create bad local minima in neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")

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)