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 "the multiplicative noise in stochastic gradient descent data dependent regularization continuous and discrete approximation"):
  Abstract: The randomness in Stochastic Gradient Descent (SGD) is considered to play a central role in the observed strong generalization capability of deep learning. In this work, we re-interpret the stochastic gradient of vanilla SGD as a matrix-vector product of the matrix of gradients and a random noise vector (namely multiplicative noise, M-Noise). Comparing to the existing theory that explains SGD using additive noise, the M-Noise helps establish a general case of SGD, namely Multiplicative SGD (M-SGD). The advantage of M-SGD is that it decouples noise from parameters, providing clear insights at the inherent randomness in SGD. Our analysis shows that 1) the M-SGD family, including the vanilla SGD, can be viewed as an minimizer with a data-dependent regularizer resemble of Rademacher complexity, which contributes to the implicit bias of M-SGD; 2) M-SGD holds a strong convergence to a continuous stochastic differential equation under the Gaussian noise assumption, ensuring the path-wise closeness of the discrete and continuous dynamics. For applications, based on M-SGD we design a fast algorithm to inject noise of different types (e.g., Gaussian and Bernoulli) into gradient descent. Based on the algorithm, we further demonstrate that M-SGD can approximate SGD with various noise types and recover the generalization performance, which reveals the potential of M-SGD to solve practical deep learning problems, e.g., large batch training with strong generalization performance. We have validated our observations on multiple practical deep learning scenarios.

Includes members:
  Member "a tail index analysis of stochastic gradient noise in deep neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "unique properties of wide minima in deep networks")
  Member "uniform in time weak error analysis for stochastic gradient descent algorithms via diffusion approximation":
    also connected through other hyperedges:
      (none)
  Member "an empirical study on regularization of deep neural networks by local rademacher complexity":
    also connected through other hyperedges:
      (none)
  Member "quasi potential as an implicit regularizer for the loss function in the stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the noisy gradient descent that generalizes as sgd")
  Member "interplay between optimization and generalization of stochastic gradient descent with covariance noise":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "three factors influencing minima in sgd":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "an alternative view when does sgd escape local minima":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "fastgae fast scalable and effective graph autoencoders with stochastic subgraph decoding")
  Member "escaping saddles with stochastic gradients":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "improve sgd training via aligning min batches")

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)