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 "toward a theory of optimization for over parameterized systems of non linear equations the lessons of deep learning"):
  Abstract: The success of deep learning is due, to a great extent, to the remarkable effectiveness of gradient-based optimization methods applied to large neural networks. In this work we isolate some general mathematical structures allowing for efficient optimization in over-parameterized systems of non-linear equations, a setting that includes deep neural networks. In particular, we show that optimization problems corresponding to such systems are not convex, even locally, but instead satisfy the Polyak-Lojasiewicz (PL) condition allowing for efficient optimization by gradient descent or SGD. We connect the PL condition of these systems to the condition number associated to the tangent kernel and develop a non-linear theory parallel to classical analyses of over-parameterized linear equations. We discuss how these ideas apply to training shallow and deep neural networks. Finally, we point out that tangent kernels associated to certain large system may be far from constant, even locally. Yet, our analysis still allows to demonstrate existence of solutions and convergence of gradient descent and SGD.

Includes members:
  Member "a jamming transition from under to over parametrization affects generalization in deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "self adaptive training beyond empirical risk minimization")
  Member "accelerating sgd with momentum for over parameterized learning":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the convergence of nesterov s accelerated gradient method in stochastic settings")
  Member "towards moderate overparameterization global convergence guarantees for training shallow neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "double descent in the condition number":
    also connected through other hyperedges:
      (none)
  Member "polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow relu networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "convergence of end to end training in deep unsupervised contrasitive learning")
  Member "finite depth and width corrections to the neural tangent kernel":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "fine grained analysis of optimization and generalization for overparameterized two layer neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "over parameterized deep neural networks have no strict local minima for any continuous activations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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)