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 "symmetry saddle points and global geometry of nonconvex matrix factorization"):
  Abstract: We propose a general theory for studying the geometry of nonconvex objective functions with underlying symmetric structures. In specific, we characterize the locations of stationary points and the null space of the associated Hessian matrices via the lens of invariant groups. As a major motivating example, we apply the proposed general theory to characterize the global geometry of the low-rank matrix factorization problem. In particular, we illustrate how the rotational symmetry group gives rise to infinitely many non-isolated strict saddle points and equivalent global minima of the objective function. By explicitly identifying all stationary points, we divide the entire parameter space into three regions: ($\cR_1$) the region containing the neighborhoods of all strict saddle points, where the objective has negative curvatures; ($\cR_2$) the region containing neighborhoods of all global minima, where the objective enjoys strong convexity along certain directions; and ($\cR_3$) the complement of the above regions, where the gradient has sufficiently large magnitudes. We further extend our result to the matrix sensing problem. This allows us to establish strong global convergence guarantees for popular iterative algorithms with arbitrary initial solutions.

Includes members:
  Member "no spurious local minima in nonconvex low rank problems a unified geometric analysis":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "no spurious local minima in deep quadratic networks")
  Member "the global optimization geometry of low rank matrix optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the non convex geometry of low rank matrix optimization")
  Member "fast algorithms for robust pca via gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems")
  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 "a geometric analysis of phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "efficient approaches for escaping higher order saddle points in non convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "necpd an online tensor decomposition with optimal stochastic gradient descent")
  Member "provable efficient online matrix completion via non convex stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "understanding the downstream instability of word embeddings")
  Member "escaping from saddle points online stochastic gradient for tensor decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "backward feature correction how deep learning performs deep learning")

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)