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 "provable limitations of deep learning"):
  Abstract: As the success of deep learning reaches more grounds, one would like to also envision the potential limits of deep learning. This paper gives a first set of results proving that certain deep learning algorithms fail at learning certain efficiently learnable functions. The results put forward a notion of cross-predictability that characterizes when such failures take place. Parity functions provide an extreme example with a cross-predictability that decays exponentially, while a mere super-polynomial decay of the cross-predictability is shown to be sufficient to obtain failures. Examples in community detection and arithmetic learning are also discussed. #R##N#Recall that it is known that the class of neural networks (NNs) with polynomial network size can express any function that can be implemented in polynomial time, and that their sample complexity scales polynomially with the network size. The challenge is with the optimization error (the ERM is NP-hard), and the success behind deep learning is to train deep NNs with descent algorithms. The failures shown in this paper apply to training poly-size NNs on function distributions of low cross-predictability with a descent algorithm that is either run with limited memory per sample or that is initialized and run with enough randomness. We further claim that such types of constraints are necessary to obtain failures, in that exact SGD with careful non-random initialization can be shown to learn parities. The cross-predictability in our results plays a similar role the statistical dimension in statistical query (SQ) algorithms, with distinctions explained in the paper. The proof techniques are based on exhibiting algorithmic constraints that imply a statistical indistinguishability between the algorithm's output on the test model v.s.\ a null model, using information measures to bound the total variation distance.

Includes members:
  Member "gradient descent for one hidden layer neural networks polynomial convergence and sq lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "poly time universality and limitations of deep learning")
  Member "extractor based time space lower bounds for learning":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "time space tradeoffs for learning from small test spaces learning low degree polynomial functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "poly time universality and limitations of deep learning")
  Member "understanding deep learning requires rethinking generalization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "distribution specific hardness of learning neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "poly time universality and limitations of deep learning")
  Member "statistical query algorithms for mean vector estimation and stochastic convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "limits on gradient compression for stochastic optimization")
  Member "train faster generalize better stability of stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  Member "delving deep into rectifiers surpassing human level performance on imagenet classification":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")

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)