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: "implicit regularization in nonconvex statistical estimation gradient descent converges linearly for phase retrieval matrix completion and blind deconvolution"
  Abstract: Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g. trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. #R##N#This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This "implicit regularization" feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e. phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a byproduct, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control --- measured entrywise and by the spectral norm --- which might be of independent interest.

Connected through hyperedge HE-1 (induced by source paper "nonconvex low rank symmetric tensor completion from noisy data"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "iterative collaborative filtering for sparse noisy tensor estimation"
    - "tensor robust principal component analysis exact recovery of corrupted low rank tensors via convex optimization"
    - "fundamental conditions for low cp rank tensor completion"
    - "exact tensor completion with sum of squares"
    - "on the optimization landscape of tensor decompositions"
    - "fast algorithms for robust pca via gradient descent"
    - "low rank tensor recovery via iterative hard thresholding"

Connected through hyperedge HE-2 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion"):
  with members:
    - "phase retrieval without small ball probability assumptions"
    - "blind deconvolution by a steepest descent algorithm on a quotient manifold"
    - "blind demixing and deconvolution at near optimal rate"
    - "low rank matrix recovery from clifford orbits"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"
    - "matrix completion has no spurious local minimum"
    - "guaranteed matrix completion via non convex factorization"
    - "optimal injectivity conditions for bilinear inverse problems with applications to identifiability of deconvolution problems"

Connected through hyperedge HE-3 (induced by source paper "gradient descent maximizes the margin of homogeneous neural networks"):
  with members:
    - "implicit regularization of discrete gradient dynamics in linear neural networks"
    - "a refined primal dual analysis of the implicit bias"
    - "implicit regularization in deep matrix factorization"
    - "fixup initialization residual learning without normalization"
    - "on exact computation with an infinitely wide neural net"
    - "implicit regularization for deep neural networks driven by an ornstein uhlenbeck like process"
    - "sorting out lipschitz function approximation"
    - "gradient descent finds global minima of deep neural networks"

Connected through hyperedge HE-4 (induced by source paper "provable low rank phase retrieval and compressive pca"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "provable subspace tracking from missing data and matrix completion"
    - "phaseless pca low rank matrix recovery from column wise phaseless measurements"
    - "provable dynamic robust pca or robust subspace tracking"
    - "low rank phase retrieval"
    - "nearly optimal robust subspace tracking"
    - "sparse phase retrieval via truncated amplitude flow"
    - "fast algorithms for robust pca via gradient descent"

Connected through hyperedge HE-5 (induced by source paper "implicit competitive regularization in gans"):
  with members:
    - "coherent gradients an approach to understanding generalization in gradient descent based optimization"
    - "what is local optimality in nonconvex nonconcave minimax optimization"
    - "on finding local nash equilibria and only local nash equilibria in zero sum games"
    - "a gradual semi discrete approach to generative network training via explicit wasserstein minimization"
    - "stochastic mirror descent on overparameterized nonlinear models convergence implicit regularization and generalization"
    - "a closer look at the optimization landscapes of generative adversarial networks"
    - "implicit regularization in deep matrix factorization"
    - "implicit regularization in over parameterized neural networks"

Connected through hyperedge HE-6 (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"

Connected through hyperedge HE-7 (induced by source paper "stochastic mirror descent on overparameterized nonlinear models convergence implicit regularization and generalization"):
  with members:
    - "stochastic gradient mirror descent minimax optimality and implicit regularization"
    - "gradient descent finds global minima of deep neural networks"
    - "overparameterized nonlinear learning gradient descent takes the shortest path"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "implicit bias of gradient descent on linear convolutional networks"
    - "a convergence theory for deep learning via over parameterization"
    - "geometry of optimization and implicit regularization in deep learning"
    - "theoretical insights into the optimization landscape of over parameterized shallow neural networks"

Connected through hyperedge HE-8 (induced by source paper "a priori estimates of the population risk for residual networks"):
  with members:
    - "learning and generalization in overparameterized neural networks going beyond two layers"
    - "exponential convergence of the deep neural network approximation for analytic functions"
    - "gradient descent finds global minima of deep neural networks"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "capacity control of relu neural networks by basis path norm"
    - "stronger generalization bounds for deep nets via a compression approach"
    - "a convergence theory for deep learning via over parameterization"
    - "gradient descent provably optimizes over parameterized neural 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.LG(Machine Learning)