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 "weight space symmetry in deep networks gives rise to permutation saddles connected by equal loss valleys across the loss landscape"):
  Abstract: The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima. In a network of $d-1$ hidden layers with $n_k$ neurons in layers $k = 1, \ldots, d$, we construct smooth paths between equivalent global minima that lead through a `permutation point' where the input and output weight vectors of two neurons in the same hidden layer $k$ collide and interchange. We show that such permutation points are critical points with at least $n_{k+1}$ vanishing eigenvalues of the Hessian matrix of second derivatives indicating a local plateau of the loss function. We find that a permutation point for the exchange of neurons $i$ and $j$ transits into a flat valley (or generally, an extended plateau of $n_{k+1}$ flat dimensions) that enables all $n_k!$ permutations of neurons in a given layer $k$ at the same loss value. Moreover, we introduce high-order permutation points by exploiting the recursive structure in neural network functions, and find that the number of $K^{\text{th}}$-order permutation points is at least by a factor $\sum_{k=1}^{d-1}\frac{1}{2!^K}{n_k-K \choose K}$ larger than the (already huge) number of equivalent global minima. In two tasks, we illustrate numerically that some of the permutation points correspond to first-order saddles (`permutation saddles'): first, in a toy network with a single hidden layer on a function approximation task and, second, in a multilayer network on the MNIST task. Our geometric approach yields a lower bound on the number of critical points generated by weight-space symmetries and provides a simple intuitive link between previous mathematical results and numerical observations.

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 "eigenvalues of the hessian in deep learning singularity and beyond":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rethinking parameter counting in deep models effective dimensionality revisited")
  Member "empirical analysis of the hessian of over parametrized neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "depth creates no bad local minima":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the global convergence of training deep linear resnets")
  Member "understanding deep learning requires rethinking generalization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "qualitatively characterizing neural network optimization problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "gradient surgery for multi task learning")
  Member "exact solutions to the nonlinear dynamics of learning in deep linear neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "transformation based adversarial video prediction on large scale data")

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)