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: "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.

Connected through hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications"):
  with members:
    - "complete dictionary learning via 120001 4 norm maximization over the orthogonal group"
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "nonconvex robust low rank matrix recovery"
    - "dual principal component pursuit probability analysis and efficient algorithms"
    - "global geometry of multichannel sparse blind deconvolution on the sphere"
    - "an overview of robust subspace recovery"
    - "subgradient descent learns orthogonal dictionaries"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"

Connected through hyperedge HE-2 (induced by source paper "toward a mathematical theory of the crystallographic phase retrieval problem"):
  with members:
    - "a note on douglas rachford subgradients and phase retrieval"
    - "phase retrieval for binary signals box relaxation and uniqueness"
    - "learning without loss"
    - "single particle cryo electron microscopy mathematical theory computational challenges and opportunities"
    - "blind phaseless short time fourier transform recovery"
    - "on signal reconstruction from frog measurements"
    - "fourier phase retrieval uniqueness and algorithms"
    - "on the uniqueness of frog methods"

Connected through hyperedge HE-3 (induced by source paper "learning a single neuron with gradient methods"):
  with members:
    - "fitting relus via sgd and quantized sgd"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "on the power and limitations of random features for understanding neural networks"
    - "a generalization theory of gradient descent for learning over parameterized deep relu networks"
    - "learning and generalization in overparameterized neural networks going beyond two layers"
    - "overparameterized nonlinear learning gradient descent takes the shortest path"
    - "beating the perils of non convexity guaranteed training of neural networks using tensor methods"
    - "learning relus via gradient descent"

Connected through hyperedge HE-4 (induced by source paper "a deterministic convergence framework for exact non convex phase retrieval"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "optimal spectral initialization for signal recovery with applications to phase retrieval"
    - "linear spectral estimators and an application to phase retrieval"
    - "phase transitions of spectral initialization for high dimensional nonconvex estimation"
    - "structured signal recovery from quadratic measurements breaking sample complexity barriers via nonconvex optimization"
    - "non convex phase retrieval from stft measurements"
    - "phasemax convex phase retrieval via basis pursuit"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"

Connected through hyperedge HE-5 (induced by source paper "revisiting landscape analysis in deep neural networks eliminating decreasing paths to infinity"):
  with members:
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "on exact computation with an infinitely wide neural net"
    - "elimination of all bad local minima in deep learning"
    - "on the convergence of adaptive gradient methods for nonconvex optimization"
    - "on the optimization of deep networks implicit acceleration by overparameterization"
    - "on the connection between learning two layers neural networks and tensor decomposition"
    - "learning one hidden layer neural networks under general input distributions"
    - "over parameterized deep neural networks have no strict local minima for any continuous activations"

Connected through hyperedge HE-6 (induced by source paper "phase retrieval of low rank matrices by anchored regression"):
  with members:
    - "blind phaseless short time fourier transform recovery"
    - "blind deconvolutional phase retrieval via convex programming"
    - "blind gain and phase calibration via sparse spectral methods"
    - "solving equations of random convex functions via anchored regression"
    - "blind deconvolution by a steepest descent algorithm on a quotient manifold"
    - "low rank phase retrieval"
    - "guaranteed blind sparse spikes deconvolution via lifting and convex optimization"
    - "self calibration via linear least squares"

Connected through hyperedge HE-7 (induced by source paper "the non convex geometry of low rank matrix optimization"):
  with members:
    - "global optimality in low rank matrix optimization"
    - "how to escape saddle points efficiently"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "low rank positive semidefinite matrix recovery from corrupted rank one measurements"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "the global optimization geometry of low rank matrix optimization"
    - "overcomplete tensor decomposition via convex optimization"
    - "finding a sparse vector in a subspace linear sparsity using alternating directions"

Connected through hyperedge HE-8 (induced by source paper "analysis of the optimization landscapes for overcomplete representation learning"):
  with members:
    - "complete dictionary learning via 120001 4 norm maximization over the orthogonal group"
    - "on the global geometry of sphere constrained sparse blind deconvolution"
    - "global geometry of multichannel sparse blind deconvolution on the sphere"
    - "convolutional dictionary learning a comparative review and new algorithms"
    - "subgradient descent learns orthogonal dictionaries"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "on the optimization landscape of tensor decompositions"
    - "how to escape saddle points efficiently"

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)