human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "a sufficient condition for convergences of adam and rmsprop"
  Abstract: Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples. Many attempts, such as decreasing an adaptive learning rate, adopting a big batch size, incorporating a temporal decorrelation technique, seeking an analogous surrogate, etc., have been tried to promote Adam/RMSProp-type algorithms to converge. In contrast with existing approaches, we introduce an alternative easy-to-check sufficient condition, which merely depends on the parameters of the base learning rate and combinations of historical second-order moments, to guarantee the global convergence of generic Adam/RMSProp for solving large-scale non-convex stochastic optimization. Moreover, we show that the convergences of several variants of Adam, such as AdamNC, AdaEMA, etc., can be directly implied via the proposed sufficient condition in the non-convex setting. In addition, we illustrate that Adam is essentially a specifically weighted AdaGrad with exponential moving average momentum, which provides a novel perspective for understanding Adam and RMSProp. This observation coupled with this sufficient condition gives much deeper interpretations on their divergences. At last, we validate the sufficient condition by applying Adam and RMSProp to tackle a certain counterexample and train deep neural networks. Numerical results are exactly in accord with our theoretical analysis.

Connected through hyperedge HE-1 (induced by source paper "non asymptotic convergence of adam type reinforcement learning algorithms under markovian sampling"):
  with members:
    - "finite time error bounds for linear stochastic approximation and td learning"
    - "an improved convergence analysis of stochastic variance reduced policy gradient"
    - "two time scale off policy td learning non asymptotic analysis over markovian samples"
    - "on the convergence proof of amsgrad and a new version"
    - "smoothing policies and safe policy gradients"
    - "finite sample analysis for sarsa with linear function approximation"
    - "characterizing the exact behaviors of temporal difference learning algorithms using markov jump linear system theory"
    - "neural temporal difference learning converges to global optima"

Connected through hyperedge HE-2 (induced by source paper "generalized embedding machines for recommender systems"):
  with members:
    - "neural factorization machines for sparse predictive analytics"
    - "attention is all you need"
    - "deep cross network for ad click predictions"
    - "strongly hierarchical factorization machines and anova kernel regression"
    - "deepfm a factorization machine based neural network for ctr prediction"
    - "attentional factorization machines learning the weight of feature interactions via attention networks"
    - "multi view machines"
    - "semi supervised classification with graph convolutional networks"

Connected through hyperedge HE-3 (induced by source paper "adamt a stochastic optimization with trend correction scheme"):
  with members:
    - "on the convergence of adam and beyond"
    - "on the convergence of adaptive gradient methods for nonconvex optimization"
    - "closing the generalization gap of adaptive gradient methods in training deep neural networks"
    - "weighted adagrad with unified momentum"
    - "on the convergence of a class of adam type algorithms for non convex optimization"
    - "decoupled weight decay regularization"
    - "fashion mnist a novel image dataset for benchmarking machine learning algorithms"
    - "an overview of gradient descent optimization algorithms"

Connected through hyperedge HE-4 (induced by source paper "on empirical comparisons of optimizers for deep learning"):
  with members:
    - "which algorithmic choices matter at which batch sizes insights from a noisy quadratic model"
    - "on the variance of the adaptive learning rate and beyond"
    - "namsg an efficient method for training neural networks"
    - "adaptive gradient methods with dynamic bound of learning rate"
    - "deepobs a deep learning optimizer benchmark suite"
    - "on the convergence of adam and beyond"
    - "efficientnet rethinking model scaling for convolutional neural networks"
    - "roberta a robustly optimized bert pretraining approach"

Connected through hyperedge HE-5 (induced by source paper "local adaalter communication efficient stochastic gradient descent with adaptive learning rates"):
  with members:
    - "error feedback fixes signsgd and other gradient compression schemes"
    - "reducing bert pre training time from 3 days to 76 minutes"
    - "communication efficient distributed blockwise momentum sgd with error feedback"
    - "large batch optimization for deep learning training bert in 76 minutes"
    - "pipe sgd a decentralized pipelined sgd framework for distributed deep net training"
    - "federated learning strategies for improving communication efficiency"
    - "don t use large mini batches use local sgd"
    - "sparsified sgd with memory"

Connected through hyperedge HE-6 (induced by source paper "blockwise adaptivity faster training and better generalization in deep learning"):
  with members:
    - "block normalized gradient method an empirical study for training deep neural network"
    - "on the convergence of weighted adagrad with momentum for training deep neural networks"
    - "closing the generalization gap of adaptive gradient methods in training deep neural networks"
    - "signsgd compressed optimisation for non convex problems"
    - "adashift decorrelation and convergence of adaptive learning rate methods"
    - "weighted adagrad with unified momentum"
    - "attention is all you need"
    - "regularizing and optimizing lstm language models"

Connected through hyperedge HE-7 (induced by source paper "escaping saddle points with adaptive gradient methods"):
  with members:
    - "on the convergence of adam and beyond"
    - "on the convergence of adaptive gradient methods for nonconvex optimization"
    - "the case for full matrix adaptive regularization"
    - "escaping saddle points in constrained optimization"
    - "adafactor adaptive learning rates with sublinear memory cost"
    - "on the convergence of a class of adam type algorithms for non convex optimization"
    - "variants of rmsprop and adagrad with logarithmic regret bounds"
    - "a generic approach for escaping saddle points"

Connected through hyperedge HE-8 (induced by source paper "global convergence of adaptive gradient methods for an over parameterized neural network"):
  with members:
    - "on the convergence of adaptive gradient methods for nonconvex optimization"
    - "gradient descent finds global minima of deep neural networks"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "closing the generalization gap of adaptive gradient methods in training deep neural networks"
    - "stochastic gradient descent optimizes over parameterized deep relu networks"
    - "signsgd compressed optimisation for non convex problems"
    - "a convergence theory for deep learning via over parameterization"
    - "on the convergence of a class of adam type algorithms for non convex optimization"

Question: Please tell me which class the center node 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)