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 "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems"):
  Abstract: We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to solving these relaxations in large-scale is the need to compute a potentially high-rank singular value decomposition (SVD) on each iteration in order to enforce the low-rank-promoting constraint. We begin by considering a simple and natural sufficient condition so that these relaxations indeed admit low-rank solutions. This condition is also necessary for a certain notion of low-rank-robustness to hold. Our main result shows that under this condition which involves the eigenvalues of the gradient vector at optimal points, SGD with mini-batches, when initialized with a "warm-start" point, produces iterates that are low-rank with high probability, and hence only a low-rank SVD computation is required on each iteration. This suggests that SGD may indeed be practically applicable to solving large-scale convex relaxations of low-rank matrix recovery problems. Our theoretical results are accompanied with supporting preliminary empirical evidence. As a side benefit, our analysis is quite simple and short.

Includes members:
  Member "fast stochastic algorithms for low rank and nonsmooth matrix problems":
    also connected through other hyperedges:
      (none)
  Member "fast algorithms for robust pca via gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "nonconvex low rank symmetric tensor completion from noisy data")
  Member "variance reduced and projection free stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "faster projection free online learning")
  Member "matrix completion has no spurious local minimum":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "provable efficient online matrix completion via non convex stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "understanding the downstream instability of word embeddings")
  Member "projection free online learning":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "faster projection free online learning")
  Member "phase retrieval via matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "making gradient descent optimal for strongly convex stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "wireless federated learning with local differential privacy")

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)