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: "phase retrieval stability and recovery guarantees"
  Abstract: We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study conditions under which x can be stably recovered from the measurements. In the noise-free setting we derive a general expression on the number of measurements needed to ensure that a unique solution can be found in a stable way, that depends on the set T through a natural complexity parameter. This parameter can be computed explicitly for many sets T of interest. For example, for k-sparse inputs we show that O(k\log(n/k)) measurements are needed, and when x can be any vector in R^n, O(n) measurements suffice. In the noisy case, we show that if one can find a value for which the empirical risk is bounded by a given, computable constant (that depends on the set T), then the error with respect to the true input is bounded above by an another, closely related complexity parameter of the set. By choosing an appropriate number N of measurements, this bound can be made arbitrarily small, and it decays at a rate faster than N^{-1/2+\delta} for any \delta>0. In particular, for k-sparse vectors stable recovery is possible from O(k\log(n/k)\log k) noisy measurements, and when x can be any vector in R^n, O(n \log n) noisy measurements suffice. We also show that the complexity parameter for the quadratic problem is the same as the one used for analyzing stability in linear measurements under very general conditions. Thus, no substantial price has to be paid in terms of stability if there is no knowledge of the phase.

Connected through hyperedge HE-1 (induced by source paper "consensus based optimization on the sphere ii convergence to global minimizers and machine learning"):
  with members:
    - "bad global minima exist and sgd can reach them"
    - "fast robust and non convex subspace recovery"
    - "a well tempered landscape for non convex robust subspace recovery"
    - "robust computation of linear models by convex relaxation"
    - "phase retrieval via wirtinger flow theory and algorithms"
    - "phase retrieval via matrix completion"

Connected through hyperedge HE-2 (induced by source paper "complex phase retrieval from subgaussian measurements"):
  with members:
    - "on the convex geometry of blind deconvolution and matrix completion"
    - "phase retrieval without small ball probability assumptions"
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"
    - "structured signal recovery from quadratic measurements breaking sample complexity barriers via nonconvex optimization"
    - "phasemax convex phase retrieval via basis pursuit"
    - "a geometric analysis of phase retrieval"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"
    - "stable low rank matrix recovery via null space properties"

Connected through hyperedge HE-3 (induced by source paper "a note on douglas rachford subgradients and phase retrieval"):
  with members:
    - "on fienup methods for sparse phase retrieval"
    - "fourier phase retrieval uniqueness and algorithms"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "non convex phase retrieval from stft measurements"
    - "the complexity of bit retrieval"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"
    - "a geometric analysis of phase retrieval"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"

Connected through hyperedge HE-4 (induced by source paper "measurement matrix design for phase retrieval based on mutual information"):
  with members:
    - "non convex phase retrieval from stft measurements"
    - "stft phase retrieval uniqueness guarantees and recovery algorithms"
    - "intensity only optical compressive imaging using a multiply scattering material and a double phase retrieval approach"
    - "almost lossless analog compression without phase information"
    - "phase retrieval via wirtinger flow theory and algorithms"
    - "phasecode fast and efficient compressive phase retrieval based on sparse graph codes"
    - "phase retrieval from coded diffraction patterns"
    - "communications inspired projection design with application to compressive sensing"

Connected through hyperedge HE-5 (induced by source paper "phase retrieval without small ball probability assumptions"):
  with members:
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"
    - "robust nonnegative sparse recovery and the nullspace property of 0 1 measurements"
    - "a partial derandomization of phaselift using spherical designs"
    - "phase retrieval with application to optical imaging"
    - "low rank matrix recovery from rank one measurements"
    - "phase retrieval from coded diffraction patterns"
    - "one bit compressed sensing with non gaussian measurements"
    - "solving quadratic equations via phaselift when there are about as many equations as unknowns"

Connected through hyperedge HE-6 (induced by source paper "on dc based methods for phase retrieval"):
  with members:
    - "phase retrieval from the norms of affine transformations"
    - "generalized phase retrieval measurement number matrix recovery and beyond"
    - "a geometric analysis of phase retrieval"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"
    - "phase retrieval an overview of recent developments"
    - "a general iterative shrinkage and thresholding algorithm for non convex regularized optimization problems"
    - "sparsity constrained nonlinear optimization optimality conditions and algorithms"

Connected through hyperedge HE-7 (induced by source paper "structured signal recovery from quadratic measurements breaking sample complexity barriers via nonconvex optimization"):
  with members:
    - "multiple illumination phaseless super resolution mips with applications to phaseless doa estimation and diffraction imaging"
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"
    - "sparse phase retrieval via truncated amplitude flow"
    - "non convex phase retrieval from stft measurements"
    - "reconstruction of signals from their autocorrelation and cross correlation vectors with applications to phase retrieval and blind channel estimation"
    - "stft phase retrieval uniqueness guarantees and recovery algorithms"
    - "compressed sensing from phaseless gaussian measurements via linear programming in the natural parameter space"
    - "phasemax convex phase retrieval via basis pursuit"

Connected through hyperedge HE-8 (induced by source paper "fourier phase retrieval uniqueness and algorithms"):
  with members:
    - "message passing algorithms for synchronization problems over compact groups"
    - "bispectrum inversion with application to multireference alignment"
    - "on fienup methods for sparse phase retrieval"
    - "on signal reconstruction from frog measurements"
    - "on the 2d phase retrieval problem"
    - "multiple illumination phaseless super resolution mips with applications to phaseless doa estimation and diffraction imaging"
    - "on the uniqueness of frog methods"
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"

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.IT(Information Theory)