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 power of interpolation understanding the effectiveness of sgd in modern over parametrized learning"):
  Abstract: In this paper we aim to formally explain the phenomenon of fast convergence of SGD observed in modern machine learning. The key observation is that most modern learning architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss (classification and regression) close to zero. While it is still unclear why these interpolated solutions perform well on test data, we show that these regimes allow for fast convergence of SGD, comparable in number of iterations to full gradient descent. #R##N#For convex loss functions we obtain an exponential convergence bound for {\it mini-batch} SGD parallel to that for full gradient descent. We show that there is a critical batch size $m^*$ such that: (a) SGD iteration with mini-batch size $m\leq m^*$ is nearly equivalent to $m$ iterations of mini-batch size $1$ (\emph{linear scaling regime}). (b) SGD iteration with mini-batch $m> m^*$ is nearly equivalent to a full gradient descent iteration (\emph{saturation regime}). #R##N#Moreover, for the quadratic loss, we derive explicit expressions for the optimal mini-batch and step size and explicitly characterize the two regimes above. The critical mini-batch size can be viewed as the limit for effective mini-batch parallelization. It is also nearly independent of the data size, implying $O(n)$ acceleration over GD per unit of computation. We give experimental evidence on real data which closely follows our theoretical analyses. #R##N#Finally, we show how our results fit in the recent developments in training deep neural networks and discuss connections to adaptive rates for SGD and variance reduction.

Includes members:
  Member "an analysis of deep neural network models for practical applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "crl class representative learning for image classification")
  Member "scaling sgd batch size to 32k for imagenet training":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "communication optimization strategies for distributed deep learning a survey")
  Member "don t decay the learning rate increase the batch size":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "communication optimization strategies for distributed deep learning a survey")
  Member "spectrally normalized margin bounds for neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "empirical analysis of the hessian of over parametrized neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "revisiting distributed synchronous sgd":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "trends and advancements in deep neural network communication")
  Member "accurate large minibatch sgd training imagenet in 1 hour":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "learning representations by predicting bags of visual words")
  Member "gradient diversity a key ingredient for scalable distributed learning":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "large batch training does not need warmup")

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)