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 "deep neural networks with multi branch architectures are less non convex"):
  Abstract: Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the multi-branch architecture is less non-convex in terms of duality gap. The duality gap measures the degree of intrinsic non-convexity of an optimization problem: smaller gap in relative value implies lower degree of intrinsic non-convexity. The challenge is to quantitatively measure the duality gap of highly non-convex problems such as deep neural networks. In this work, we provide strong guarantees of this quantity for two classes of network architectures. For the neural networks with arbitrary activation functions, multi-branch architecture and a variant of hinge loss, we show that the duality gap of both population and empirical risks shrinks to zero as the number of branches increases. This result sheds light on better understanding the power of over-parametrization where increasing the network width tends to make the loss surface less non-convex. For the neural networks with linear activation function and $\ell_2$ loss, we show that the duality gap of empirical risk is zero. Our two results work for arbitrary depths and adversarial data, while the analytical techniques might be of independent interest to non-convex optimization more broadly. Experiments on both synthetic and real-world datasets validate our results.

Includes members:
  Member "on the optimization of deep networks implicit acceleration by overparameterization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "train large then compress rethinking model size for efficient training and inference of transformers")
  Member "towards understanding the role of over parametrization in generalization of neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the implicit and explicit regularization effects of dropout")
  Member "on the power of over parametrization in neural networks with quadratic activation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "knowledge distillation via adaptive instance normalization")
  Member "learning one hidden layer neural networks with landscape design":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "matrix completion and related problems via strong duality":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "testing matrix rank optimally")
  Member "mathematics of deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "translating diffusion wavelets and regularisation into residual networks")
  Member "theoretical insights into the optimization landscape of over parameterized shallow neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "failures of gradient based deep learning":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "regularizing activations in neural networks via distribution matching with the wasserstein metric")

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)