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 "complete dictionary recovery over the sphere i overview and the geometric picture"):
  Abstract: We consider the problem of recovering a complete (i.e., square and invertible) matrix    $ A_{0}$   , from    $ Y \in \mathbb R ^{n \times p}$    with    $ Y = A_{0} X_{0}$   , provided    $ X_{0}$    is sufficiently sparse. This recovery problem is central to theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers    $ A_{0}$    when    $ X_{0}$    has    $O \left ({ n }\right )$    nonzeros per column, under suitable probability model for    $ X_{0}$   . In contrast, prior results based on efficient algorithms either only guarantee recovery when    $ X_{0}$    has    $O(\sqrt {n})$    zeros per column, or require multiple rounds of semidefinite programming relaxation to work when    $ X_{0}$    has    $O(n)$    nonzeros per column. Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint. In this paper, we provide a geometric characterization of the objective landscape. In particular, we show that the problem is highly structured with high probability: 1) there are no “spurious” local minimizers and 2) around all saddle points the objective has a negative directional curvature. This distinctive structure makes the problem amenable to efficient optimization algorithms. In a companion paper, we design a second-order trust-region algorithm over the sphere that provably converges to a local minimizer from arbitrary initializations, despite the presence of saddle points.

Includes members:
  Member "complete dictionary recovery over the sphere ii recovery by riemannian trust region method":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "polynomial time tensor decompositions with sum of squares":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "efficiently learning structured distributions from untrusted batches")
  Member "finding a sparse vector in a subspace linear sparsity using alternating directions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "matrix completion has no spurious local minimum":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "guaranteed matrix completion via non convex factorization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "a geometric analysis of phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "optimal injectivity conditions for bilinear inverse problems with applications to identifiability of deconvolution problems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion")
  Member "simple efficient and neural algorithms for sparse coding":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "convolutional dictionary learning based auto encoders for natural exponential family distributions")

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.IT(Information Theory)