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 "a geometric analysis of phase retrieval"):
  Abstract: Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of $m$ measurements, $y_k = |\mathbf a_k^* \mathbf x|$ for $k = 1, \dots, m$, is it possible to recover $\mathbf x \in \mathbb{C}^n$ (i.e., length-$n$ complex vector)? This **generalized phase retrieval** (GPR) problem is a fundamental task in various disciplines, and has been the subject of much recent investigation. Natural nonconvex heuristics often work remarkably well for GPR in practice, but lack clear theoretical explanations. In this paper, we take a step towards bridging this gap. We prove that when the measurement vectors $\mathbf a_k$'s are generic (i.i.d. complex Gaussian) and the number of measurements is large enough ($m \ge C n \log^3 n$), with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) there are no spurious local minimizers, and all global minimizers are equal to the target signal $\mathbf x$, up to a global phase; and (2) the objective function has a negative curvature around each saddle point. This structure allows a number of iterative optimization methods to efficiently find a global minimizer, without special initialization. To corroborate the claim, we describe and analyze a second-order trust-region algorithm.

Includes members:
  Member "non convex phase retrieval from stft measurements":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "toward a mathematical theory of the crystallographic phase retrieval problem")
  Member "phasemax convex phase retrieval via basis pursuit":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "deep s 3 pr simultaneous source separation and phase retrieval using deep generative models")
  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 "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 "phase retrieval via incremental truncated wirtinger flow":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "implicit regularization in nonconvex statistical estimation gradient descent converges linearly for phase retrieval matrix completion and blind deconvolution")
  Member "phaseless rcovery using gauss newton method":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "implicit regularization in nonconvex statistical estimation gradient descent converges linearly for phase retrieval matrix completion and blind deconvolution")

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)