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 "algorithmic theory of odes and sampling from well conditioned logconcave densities"):
  Abstract: Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have dimension-independent bounds for the underlying $\mathit{continuous}$ processes under sufficiently strong smoothness conditions, the resulting discrete algorithms have complexity and number of function evaluations growing with the dimension. Motivated by this problem, in this paper, we give a general algorithm for solving multivariate ordinary differential equations whose solution is close to the span of a known basis of functions (e.g., polynomials or piecewise polynomials). The resulting algorithm has polylogarithmic depth and essentially tight runtime - it is nearly linear in the size of the representation of the solution. #R##N#We apply this to the sampling problem to obtain a nearly linear implementation of HMC for a broad class of smooth, strongly logconcave densities, with the number of iterations (parallel depth) and gradient evaluations being $\mathit{polylogarithmic}$ in the dimension (rather than polynomial as in previous work). This class includes the widely-used loss function for logistic regression with incoherent weight matrices and has been subject of much study recently. We also give a faster algorithm with $ \mathit{polylogarithmic~depth}$ for the more general and standard class of strongly convex functions with Lipschitz gradient. These results are based on (1) an improved contraction bound for the exact HMC process and (2) logarithmic bounds on the degree of polynomials that approximate solutions of the differential equations arising in implementing HMC.

Includes members:
  Member "dimensionally tight running time bounds for second order hamiltonian monte carlo":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "nonconvex sampling with the metropolis adjusted langevin algorithm")
  Member "relative error tensor low rank approximation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "non convex learning via stochastic gradient langevin dynamics a nonasymptotic analysis":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "an empirical study of large batch stochastic gradient descent with structured covariance noise")
  Member "a hitting time analysis of stochastic gradient langevin dynamics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient active learning of sparse halfspaces with arbitrary bounded noise")
  Member "convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "strong self concordance and sampling")
  Member "geodesic walks in polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the approximability of weighted model integration on dnf structures")
  Member "new frameworks for offline and streaming coreset constructions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sets clustering")
  Member "input sparsity and hardness for robust subspace approximation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sketching transformed matrices with applications to natural language processing")

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.DS(Data Structures and Algorithms)