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 "analysis of the optimization landscapes for overcomplete representation learning"):
  Abstract: We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many applications in high-dimensional data analysis. Despite the empirical success of simple nonconvex algorithms, theoretical justifications of why these methods work so well are far from satisfactory. In this work, we show these problems can be formulated as $\ell^4$-norm optimization problems with spherical constraint, and study the geometric properties of their nonconvex optimization landscapes. For both problems, we show the nonconvex objectives have benign (global) geometric structures, in the sense that every local minimizer is close to one of the target solutions and every saddle point exhibits negative curvature. This discovery enables the development of guaranteed global optimization methods using simple initializations. For both problems, we show the nonconvex objectives have benign geometric structures -- every local minimizer is close to one of the target solutions and every saddle point exhibits negative curvature -- either in the entire space or within a sufficiently large region. This discovery ensures local search algorithms (such as Riemannian gradient descent) with simple initializations approximately find the target solutions. Finally, numerical experiments justify our theoretical discoveries.

Includes members:
  Member "complete dictionary learning via 120001 4 norm maximization over the orthogonal group":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "on the global geometry of sphere constrained sparse blind deconvolution":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "interference removal for radar communication co existence the random scattering case")
  Member "global geometry of multichannel sparse blind deconvolution on the sphere":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "convolutional dictionary learning a comparative review and new algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "convolutional dictionary learning based auto encoders for natural exponential family distributions")
  Member "subgradient descent learns orthogonal dictionaries":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "complete dictionary recovery over the sphere i overview and the geometric picture":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "on the optimization landscape of tensor decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "nonconvex low rank symmetric tensor completion from noisy data")
  Member "how to escape saddle points efficiently":
    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)