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 gap between strict saddles and true convexity an omega log d lower bound for eigenvector approximation"):
  Abstract: We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact} queries of the form $w^{(i)} = Mv^{(i)}$ for $i \in \{1,\dots,T\}$, where $v^{(i)}$ is drawn from a distribution which depends arbitrarily on the past queries and measurements $\{v^{(j)},w^{(j)}\}_{1 \le j \le i-1}$. We show that for a small constant $\epsilon$, any adaptive, randomized algorithm which can find a unit vector $\widehat{v}$ for which $\widehat{v}^{\top}M\widehat{v} \ge (1-\epsilon)\|M\|$, with even small probability, must make $T = \Omega(\log d)$ queries. In addition to settling a widely-held folk conjecture, this bound demonstrates a fundamental gap between convex optimization and "strict-saddle" non-convex optimization of which PCA is a canonical example: in the former, first-order methods can have dimension-free iteration complexity, whereas in PCA, the iteration complexity of gradient-based methods must necessarily grow with the dimension. Our argument proceeds via a reduction to estimating the rank-one spike in a deformed Wigner model. We establish lower bounds for this model by developing a "truncated" analogue of the $\chi^2$ Bayes-risk lower bound of Chen et al.

Includes members:
  Member "communication efficient algorithms for distributed stochastic principal component analysis":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "complete dictionary recovery over the sphere i overview and the geometric picture":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "beating the perils of non convexity guaranteed training of neural networks using tensor methods":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "no spurious local minima in deep quadratic networks")
  Member "optimal lower bounds for universal relation samplers and finding duplicates":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "tight query complexity lower bounds for pca via finite sample deformed wigner law")
  Member "lifting randomized query complexity to randomized communication complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "complexity theory game theory and economics the barbados lectures")
  Member "how to escape saddle points efficiently":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "the simulator understanding adaptive sampling in the moderate confidence regime":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sequential mode estimation with oracle queries")
  Member "low rank approximation with entrywise ell_1 norm error":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sketching transformed matrices with applications to natural language processing")

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)