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 under a generative prior"
  Abstract: The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to a known basis, and the generic sparsity prior is enforced via $\ell_1$ regularization. While successful in the realm of linear inverse problems, such $\ell_1$ methods have encountered possibly fundamental limitations, as no computationally efficient algorithm for phase retrieval of a $k$-sparse signal has been proven to succeed with fewer than $O(k^2\log n)$ generic measurements, exceeding the theoretical optimum of $O(k \log n)$. In this paper, we propose a novel framework for phase retrieval by 1) modeling natural signals as being in the range of a deep generative neural network $G : \mathbb{R}^k \rightarrow \mathbb{R}^n$ and 2) enforcing this prior directly by optimizing an empirical risk objective over the domain of the generator. Our formulation has provably favorable global geometry for gradient methods, as soon as $m = O(kd^2\log n)$, where $d$ is the depth of the network. Specifically, when suitable deterministic conditions on the generator and measurement matrix are met, we construct a descent direction for any point outside of a small neighborhood around the unique global minimizer and its negative multiple, and show that such conditions hold with high probability under Gaussian ensembles of multilayer fully-connected generator networks and measurement matrices. This formulation for structured phase retrieval thus has two advantages over sparsity based methods: 1) deep generative priors can more tightly represent natural signals and 2) information theoretically optimal sample complexity. We corroborate these results with experiments showing that exploiting generative models in phase retrieval tasks outperforms sparse phase retrieval methods.

Connected through hyperedge HE-1 (induced by source paper "deep s 3 pr simultaneous source separation and phase retrieval using deep generative models"):
  with members:
    - "deep compressed sensing"
    - "alternating phase projected gradient descent with generative priors for solving compressive phase retrieval"
    - "invertible generative models for inverse problems mitigating representation error and dataset bias"
    - "fast and provable admm for learning with generative priors"
    - "blind phaseless short time fourier transform recovery"
    - "deep ptych subsampled fourier ptychography using generative priors"
    - "blind image deconvolution using deep generative priors"
    - "robust compressive phase retrieval via deep generative priors"

Connected through hyperedge HE-2 (induced by source paper "sub gaussian matrices on sets optimal tail dependence and applications"):
  with members:
    - "global guarantees for enforcing deep generative priors by empirical risk"
    - "from compressed sensing to compressed bit streams practical encoders tractable decoders"
    - "why are deep nets reversible a simple theory with implications for training"
    - "compressive sensing with redundant dictionaries and structured measurements"
    - "randomized sketches of convex programs with sharp guarantees"
    - "sketching as a tool for numerical linear algebra"
    - "dimensionality reduction with subgaussian matrices a unified theory"
    - "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction"

Connected through hyperedge HE-3 (induced by source paper "fast and provable admm for learning with generative priors"):
  with members:
    - "gansynth adversarial neural audio synthesis"
    - "algorithmic aspects of inverse problems using generative models"
    - "memorization precedes generation learning unsupervised gans with memory networks"
    - "defense gan protecting classifiers against adversarial attacks using generative models"
    - "deep denoising rate optimal recovery of structured signals with a deep prior"
    - "large scale gan training for high fidelity natural image synthesis"
    - "adversarial audio synthesis"
    - "correction by projection denoising images with generative adversarial networks"

Connected through hyperedge HE-4 (induced by source paper "denoising and regularization via exploiting the structural bias of convolutional generators"):
  with members:
    - "generalization guarantees for neural networks via harnessing the low rank structure of the jacobian"
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "algorithmic guarantees for inverse imaging with untrained network priors"
    - "regularizing linear inverse problems with convolutional neural networks"
    - "the convergence rate of neural networks for learned functions of different frequencies"
    - "gradient descent with early stopping is provably robust to label noise for overparameterized neural networks"
    - "fine grained analysis of optimization and generalization for overparameterized two layer neural networks"
    - "rate optimal denoising with deep neural networks"

Connected through hyperedge HE-5 (induced by source paper "algorithmic guarantees for inverse imaging with untrained network priors"):
  with members:
    - "towards moderate overparameterization global convergence guarantees for training shallow neural networks"
    - "deep compressed sensing"
    - "regularizing linear inverse problems with convolutional neural networks"
    - "alternating phase projected gradient descent with generative priors for solving compressive phase retrieval"
    - "one dimensional deep image prior for time series inverse problems"
    - "audio denoising with deep network priors"
    - "deep decoder concise image representations from untrained non convolutional networks"
    - "multilayer convolutional sparse modeling pursuit and dictionary learning"

Connected through hyperedge HE-6 (induced by source paper "invertible generative models for inverse problems mitigating representation error and dataset bias"):
  with members:
    - "medical image synthesis for data augmentation and anonymization using generative adversarial networks"
    - "analyzing inverse problems with invertible neural networks"
    - "deep decoder concise image representations from untrained non convolutional networks"
    - "finger gan generating realistic fingerprint images using connectivity imposed gan"
    - "latent convolutional models"
    - "blind image deconvolution using deep generative priors"
    - "i revnet deep invertible networks"
    - "the reversible residual network backpropagation without storing activations"

Connected through hyperedge HE-7 (induced by source paper "alternating phase projected gradient descent with generative priors for solving compressive phase retrieval"):
  with members:
    - "robust compressive phase retrieval via deep generative priors"
    - "began boundary equilibrium generative adversarial networks"
    - "image restoration by iterative denoising and backward projections"
    - "improved recovery guarantees for phase retrieval from coded diffraction patterns"
    - "learning deep cnn denoiser prior for image restoration"
    - "sparse phase retrieval via truncated amplitude flow"
    - "unsupervised representation learning with deep convolutional generative adversarial networks"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"

Connected through hyperedge HE-8 (induced by source paper "inverting deep generative models one layer at a time"):
  with members:
    - "asymptotics of map inference in deep networks"
    - "rate optimal denoising with deep neural networks"
    - "deep decoder concise image representations from untrained non convolutional networks"
    - "random mesh projectors for inverse problems"
    - "neural proximal gradient descent for compressive imaging"
    - "sunlayer stable denoising with generative networks"
    - "deep denoising rate optimal recovery of structured signals with a deep prior"
    - "correction by projection denoising images with generative adversarial networks"

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)