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 "empirical analysis of the hessian of over parametrized neural networks"):
  Abstract: We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Includes members:
  Member "three factors influencing minima in sgd":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "eigenvalues of the hessian in deep learning singularity and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rethinking parameter counting in deep models effective dimensionality revisited")
  Member "sharp minima can generalize for deep nets":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "bayesian deep learning and a probabilistic perspective of generalization")
  Member "opening the black box of deep neural networks via information":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the information bottleneck problems models connections applications and information theoretic views")
  Member "accurate large minibatch sgd training imagenet in 1 hour":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "learning representations by predicting bags of visual words")
  Member "understanding deep learning requires rethinking generalization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "entropy sgd biasing gradient descent into wide valleys":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "bayesian deep learning and a probabilistic perspective of generalization")
  Member "training recurrent neural networks by diffusion":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "adaptive regularization via residual smoothing in deep learning optimization")

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)