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 "solving random quadratic systems of equations is nearly as easy as solving linear systems"):
  Abstract: We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We propose a novel method, which starting with an initial guess computed by means of a spectral method, proceeds by minimizing a nonconvex functional as in the Wirtinger flow approach. There are several key distinguishing features, most notably, a distinct objective functional and novel update rules, which operate in an adaptive fashion and drop terms bearing too much influence on the search direction. These careful selection rules provide a tighter initial guess, better descent directions, and thus enhanced practical performance. On the theoretical side, we prove that for certain unstructured models of quadratic systems, our algorithms return the correct solution in linear time, i.e. in time proportional to reading the data $\{\boldsymbol{a}_i\}$ and $\{y_i\}$ as soon as the ratio $m/n$ between the number of equations and unknowns exceeds a fixed numerical constant. We extend the theory to deal with noisy systems in which we only have $y_i \approx |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$ and prove that our algorithms achieve a statistical accuracy, which is nearly un-improvable. We complement our theoretical study with numerical examples showing that solving random quadratic systems is both computationally and statistically not much harder than solving linear systems of the same size---hence the title of this paper. For instance, we demonstrate empirically that the computational cost of our algorithm is about four times that of solving a least-squares problem of the same size.

Includes members:
  Member "improved recovery guarantees for phase retrieval from coded diffraction patterns":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "complex phase retrieval from subgaussian measurements")
  Member "guaranteed matrix completion via non convex factorization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "simple efficient and neural algorithms for sparse coding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "convolutional dictionary learning based auto encoders for natural exponential family distributions")
  Member "a partial derandomization of phaselift using spherical designs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "complex phase retrieval from subgaussian measurements")
  Member "compressive phase retrieval via generalized approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "complete dictionary recovery over the sphere":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "efficient compressive phase retrieval with constrained sensing vectors":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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-8 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")

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)