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 "measure manifold learning and optimization a theory of neural networks"):
  Abstract: We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. #R##N#* Built on the formalism of probability coupling theory, we derive an algorithm framework, named Hierarchical Measure Group and Approximate System (HMGAS), nicknamed S-System, that is designed to learn the complex hierarchical, statistical dependency in the physical world. #R##N#* We show that NNs are special cases of S-System when the probability kernels assume certain exponential family distributions. Activation Functions are derived formally. We further endow geometry on NNs through information geometry, show that intermediate feature spaces of NNs are stochastic manifolds, and prove that "distance" between samples is contracted as layers stack up. #R##N#* S-System shows NNs are inherently stochastic, and under a set of realistic boundedness and diversity conditions, it enables us to prove that for large size nonlinear deep NNs with a class of losses, including the hinge loss, all local minima are global minima with zero loss errors, and regions around the minima are flat basins where all eigenvalues of Hessians are concentrated around zero, using tools and ideas from mean field theory, random matrix theory, and nonlinear operator equations. #R##N#* S-System, the information-geometry structure and the optimization behaviors combined completes the analog between Renormalization Group (RG) and NNs. It shows that a NN is a complex adaptive system that estimates the statistic dependency of microscopic object, e.g., pixels, in multiple scales. Unlike clear-cut physical quantity produced by RG in physics, e.g., temperature, NNs renormalize/recompose manifolds emerging through learning/optimization that divide the sample space into highly semantically meaningful groups that are dictated by supervised labels (in supervised NNs).

Includes members:
  Member "theoretical impediments to machine learning with seven sparks from the causal revolution":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "causal interpretability for machine learning problems methods and evaluation")
  Member "expectation propagation a probabilistic view of deep feed forward networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rice classification using spatio spectral deep convolutional neural network")
  Member "theory iiib generalization in deep networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "think global act local relating dnn generalisation and node level snr")
  Member "optimization landscape and expressivity of deep cnns":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "global convergence of deep networks with one wide layer followed by pyramidal topology")
  Member "deep linear neural networks with arbitrary loss all local minima are global":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "searching for activation functions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "the loss surface of deep and wide neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "translating diffusion wavelets and regularisation into residual networks")
  Member "global optimality conditions for deep neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the global convergence of training deep linear resnets")

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)