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 "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.

Includes members:
  Member "sparse phase retrieval via truncated amplitude flow":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "provable low rank phase retrieval and compressive pca")
  Member "a geometric analysis of phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "why are deep nets reversible a simple theory with implications for training":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "privacy preserving learning via deep net pruning")
  Member "efficient compressive phase retrieval with constrained sensing vectors":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "alternating phase projected gradient descent with generative priors for solving compressive phase retrieval")
  Member "phase retrieval via wirtinger flow theory and algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "adam a method for stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "deep learning face attributes in the wild":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "deepfakes and beyond a survey of face manipulation and fake detection")
  Member "sparse phase retrieval convex algorithms and limitations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the capacity of waveform channels under square law detection of time limited signals")

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)