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作者：Foss, Sergey; Konstantopoulos, Takis; Pyatkin, Artem
作者单位：Heriot Watt University; University of Liverpool; Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：To each edge (i, j), i < j, of the complete directed graph on the integers we assign unit weight with probability p or weight x with probability 1 - p, independently from edge to edge, and give to each path weight equal to the sum of its edge weights. If Wx0,n is the maximum weight of all paths from 0 to n then Wx0,n/n -> Cp(x), as n -> infinity, almost surely, where Cp(x)is positive and deterministic. We study Cp(x) as a function of x, for fixed 0 < p < 1, and show that it is a strictly incre...
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作者：Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-pablo
作者单位：University of Munich; University of Warwick; Nanyang Technological University
摘要：This work studies approximation based on single-hidden-layer feed -forward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hy-perparameters are optimized, have been successfully applied in a wide range of static and dynamic learning problems. Despite the popularity of this ap-proach in empirical tasks, important theoretical questions regarding the rela-tion between the unknown function, the weight distribu...
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作者：Blanca, Antonio; Gheissari, Reza
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge probability p is an element of (0,1) and a cluster weight q > 0. We establish that for every q >= 1, the random-cluster Glauber dynamics mixes in optimal Theta(n log n) steps on n-vertex random graphs having a prescribed degree sequence with bounded average branc...
