human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "matrix completion has no spurious local minimum"
  Abstract: Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in proving various non-convex algorithms converge from a good initial point, it remains unclear why random or arbitrary initialization suffices in practice. We prove that the commonly used non-convex objective function for \textit{positive semidefinite} matrix completion has no spurious local minima --- all local minima must also be global. Therefore, many popular optimization algorithms such as (stochastic) gradient descent can provably solve positive semidefinite matrix completion with \textit{arbitrary} initialization in polynomial time. The result can be generalized to the setting when the observed entries contain noise. We believe that our main proof strategy can be useful for understanding geometric properties of other statistical problems involving partial or noisy observations.

Connected through hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications"):
  with members:
    - "complete dictionary learning via 120001 4 norm maximization over the orthogonal group"
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "nonconvex robust low rank matrix recovery"
    - "dual principal component pursuit probability analysis and efficient algorithms"
    - "global geometry of multichannel sparse blind deconvolution on the sphere"
    - "an overview of robust subspace recovery"
    - "subgradient descent learns orthogonal dictionaries"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"

Connected through hyperedge HE-2 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks"):
  with members:
    - "depth creates no more spurious local minima"
    - "on connected sublevel sets in deep learning"
    - "elimination of all bad local minima in deep learning"
    - "small nonlinearities in activation functions create bad local minima in neural networks"
    - "learning one hidden layer neural networks under general input distributions"
    - "over parameterized deep neural networks have no strict local minima for any continuous activations"
    - "gradient descent finds global minima of deep neural networks"
    - "on the loss landscape of a class of deep neural networks with no bad local valleys"

Connected through hyperedge HE-3 (induced by source paper "no spurious local minima in deep quadratic networks"):
  with members:
    - "on the connection between learning two layers neural networks and tensor decomposition"
    - "polynomial regression as an alternative to neural nets"
    - "universal approximation with quadratic deep networks"
    - "beating the perils of non convexity guaranteed training of neural networks using tensor methods"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "recovery guarantees for one hidden layer neural networks"
    - "theoretical insights into the optimization landscape of over parameterized shallow neural networks"
    - "convergence results for neural networks via electrodynamics"

Connected through hyperedge HE-4 (induced by source paper "recommendation on a budget column space recovery from partially observed entries with random or active sampling"):
  with members:
    - "probabilistic tools for the analysis of randomized optimization heuristics"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "streaming principal component analysis from incomplete data"
    - "subspace learning with partial information"
    - "understanding alternating minimization for matrix completion"
    - "faster subset selection for matrices and applications"
    - "the power of convex relaxation near optimal matrix completion"
    - "matrix completion from noisy entries"

Connected through hyperedge HE-5 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems"):
  with members:
    - "fast stochastic algorithms for low rank and nonsmooth matrix problems"
    - "fast algorithms for robust pca via gradient descent"
    - "variance reduced and projection free stochastic optimization"
    - "provable efficient online matrix completion via non convex stochastic gradient descent"
    - "projection free online learning"
    - "phase retrieval via matrix completion"
    - "making gradient descent optimal for strongly convex stochastic optimization"
    - "a simpler approach to matrix completion"

Connected through hyperedge HE-6 (induced by source paper "thresholds of descending algorithms in inference problems"):
  with members:
    - "passed spurious descent algorithms and local minima in spiked matrix tensor models"
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "marvels and pitfalls of the langevin algorithm in noisy high dimensional inference"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "message passing algorithms for compressed sensing"

Connected through hyperedge HE-7 (induced by source paper "convergence to second order stationarity for non negative matrix factorization provably and concurrently"):
  with members:
    - "how to escape saddle points efficiently"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "descent methods for nonnegative matrix factorization"
    - "computing a nonnegative matrix factorization provably"
    - "on the complexity of nonnegative matrix factorization"

Connected through hyperedge HE-8 (induced by source paper "revisiting landscape analysis in deep neural networks eliminating decreasing paths to infinity"):
  with members:
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "on exact computation with an infinitely wide neural net"
    - "elimination of all bad local minima in deep learning"
    - "on the convergence of adaptive gradient methods for nonconvex optimization"
    - "on the optimization of deep networks implicit acceleration by overparameterization"
    - "on the connection between learning two layers neural networks and tensor decomposition"
    - "learning one hidden layer neural networks under general input distributions"
    - "over parameterized deep neural networks have no strict local minima for any continuous activations"

Question: Please tell me which class the center node 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)