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: "on the local minima of the empirical risk"
  Abstract: Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population risk is generally significantly more well-behaved from an optimization point of view than the empirical risk. In particular, sampling can create many spurious local minima. We consider a general framework which aims to optimize a smooth nonconvex function $F$ (population risk) given only access to an approximation $f$ (empirical risk) that is pointwise close to $F$ (i.e., $\|F-f\|_{\infty} \le \nu$). Our objective is to find the $\epsilon$-approximate local minima of the underlying function $F$ while avoiding the shallow local minima---arising because of the tolerance $\nu$---which exist only in $f$. We propose a simple algorithm based on stochastic gradient descent (SGD) on a smoothed version of $f$ that is guaranteed to achieve our goal as long as $\nu \le O(\epsilon^{1.5}/d)$. We also provide an almost matching lower bound showing that our algorithm achieves optimal error tolerance $\nu$ among all algorithms making a polynomial number of queries of $f$. As a concrete example, we show that our results can be directly used to give sample complexities for learning a ReLU unit.

Connected through hyperedge HE-1 (induced by source paper "asymmetric valleys beyond sharp and flat local minima"):
  with members:
    - "towards understanding the role of over parametrization in generalization of neural networks"
    - "the loss landscape of overparameterized neural networks"
    - "stronger generalization bounds for deep nets via a compression approach"
    - "three factors influencing minima in sgd"
    - "averaging weights leads to wider optima and better generalization"
    - "risk and parameter convergence of logistic regression"
    - "revisiting small batch training for deep neural networks"
    - "how to make the gradients small stochastically"

Connected through hyperedge HE-2 (induced by source paper "towards moderate overparameterization global convergence guarantees for training shallow neural networks"):
  with members:
    - "on the optimization of deep networks implicit acceleration by overparameterization"
    - "learning and generalization in overparameterized neural networks going beyond two layers"
    - "gradient descent finds global minima of deep neural networks"
    - "overparameterized nonlinear learning gradient descent takes the shortest path"
    - "the global optimization geometry of shallow linear neural networks"
    - "stochastic gradient descent learns state equations with nonlinear activations"
    - "learning overparameterized neural networks via stochastic gradient descent on structured data"
    - "gradient descent aligns the layers of deep linear networks"

Connected through hyperedge HE-3 (induced by source paper "solving empirical risk minimization in the current matrix multiplication time"):
  with members:
    - "nearly sample optimal sparse fourier transform in any dimension ripless and filterless"
    - "limits on all known and some unknown approaches to matrix multiplication"
    - "solving linear programs in the current matrix multiplication time"
    - "limits on the universal method for matrix multiplication"
    - "guaranteed sufficient decrease for variance reduced stochastic gradient descent"
    - "empirical risk minimization for stochastic convex optimization o 1 n and o 1 n 2 type of risk bounds"
    - "variance reduced stochastic gradient descent with sufficient decrease"
    - "improved rectangular matrix multiplication using powers of the coppersmith winograd tensor"

Connected through hyperedge HE-4 (induced by source paper "towards understanding the importance of noise in training neural networks"):
  with members:
    - "an alternative view when does sgd escape local minima"
    - "gradient descent learns one hidden layer cnn don t be afraid of spurious local minima"
    - "globally optimal gradient descent for a convnet with gaussian inputs"
    - "recovery guarantees for one hidden layer neural networks"
    - "an analytical formula of population gradient for two layered relu network and its applications in convergence and critical point analysis"
    - "how to escape saddle points efficiently"
    - "convergence analysis of two layer neural networks with relu activation"
    - "understanding deep learning requires rethinking generalization"

Connected through hyperedge HE-5 (induced by source paper "quasi potential as an implicit regularizer for the loss function in the stochastic gradient descent"):
  with members:
    - "an alternative view when does sgd escape local minima"
    - "escaping saddles with stochastic gradients"
    - "stochastic modified equations and dynamics of stochastic gradient algorithms i mathematical foundations"
    - "geometry of optimization and implicit regularization in deep learning"
    - "opening the black box of deep neural networks via information"
    - "how to escape saddle points efficiently"
    - "understanding deep learning requires rethinking generalization"
    - "on large batch training for deep learning generalization gap and sharp minima"

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)