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 "convex duality of deep neural networks"):
  Abstract: We study regularized deep neural networks and introduce an analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weight matrices for a norm regularized deep neural network training problem can be explicitly found as the extreme points of a convex set. For two-layer linear networks, we first formulate a convex dual program and prove that strong duality holds. We then extend our derivations to prove that strong duality also holds for certain deep networks. In particular, for linear deep networks, we show that each optimal layer weight matrix is rank-one and aligns with the previous layers when the network output is scalar. We also extend our analysis to the vector outputs and other convex loss functions. More importantly, we show that the same characterization can also be applied to deep ReLU networks with rank-one inputs, where we prove that strong duality still holds and optimal layer weight matrices are rank-one for scalar output networks. As a corollary, we prove that norm regularized deep ReLU networks yield spline interpolation for one-dimensional datasets which was previously known only for two-layer networks. We then verify our theoretical results via several numerical experiments.

Includes members:
  Member "width provably matters in optimization for deep linear neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "implicit regularization in deep matrix factorization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "on the optimization of deep networks implicit acceleration by overparameterization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "exponential convergence time of gradient descent for one dimensional deep linear neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the global convergence of training deep linear resnets")
  Member "implicit bias of gradient descent on linear convolutional networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "gradient descent aligns the layers of deep linear networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the global convergence of training deep linear resnets")
  Member "a convergence analysis of gradient descent for deep linear neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "deep linear neural networks with arbitrary loss all local minima are global":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")

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.LG(Machine Learning)