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 "depth separations in neural networks what is actually being separated"):
  Abstract: Existing depth separation results for constant-depth networks essentially show that certain radial functions in $\mathbb{R}^d$, which can be easily approximated with depth $3$ networks, cannot be approximated by depth $2$ networks, even up to constant accuracy, unless their size is exponential in $d$. However, the functions used to demonstrate this are rapidly oscillating, with a Lipschitz parameter scaling polynomially with the dimension $d$ (or equivalently, by scaling the function, the hardness result applies to $\mathcal{O}(1)$-Lipschitz functions only when the target accuracy $\epsilon$ is at most $\text{poly}(1/d)$). In this paper, we study whether such depth separations might still hold in the natural setting of $\mathcal{O}(1)$-Lipschitz radial functions, when $\epsilon$ does not scale with $d$. Perhaps surprisingly, we show that the answer is negative: In contrast to the intuition suggested by previous work, it \emph{is} possible to approximate $\mathcal{O}(1)$-Lipschitz radial functions with depth $2$, size $\text{poly}(d)$ networks, for every constant $\epsilon$. We complement it by showing that approximating such functions is also possible with depth $2$, size $\text{poly}(1/\epsilon)$ networks, for every constant $d$. Finally, we show that it is not possible to have polynomial dependence in both $d,1/\epsilon$ simultaneously. Overall, our results indicate that in order to show depth separations for expressing $\mathcal{O}(1)$-Lipschitz functions with constant accuracy -- if at all possible -- one would need fundamentally different techniques than existing ones in the literature.

Includes members:
  Member "provable limitations of deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "poly time universality and limitations of deep learning")
  Member "on the complexity of learning neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "failures of gradient based deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "regularizing activations in neural networks via distribution matching with the wasserstein metric")
  Member "depth separation for neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "error bounds for approximations with deep relu networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "neural contextual bandits with ucb based exploration")
  Member "distribution specific hardness of learning neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "poly time universality and limitations of deep learning")
  Member "benefits of depth in neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "lossless compression of deep neural networks")
  Member "why deep neural networks for function approximation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "neural contextual bandits with ucb based exploration")

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)