The generalization advantage of SGD over random sampling diminishes with growing training set size in binary networks, as measured by joint density of states over train and test accuracy.
Betancourt,Identifying the optimal integration time in hamiltonian monte carlo, 1601.00225
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abstract
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this paper I show how the geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of these parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called \emph{Exhaustive Hamiltonian Monte Carlo} before demonstrating the utility of these ideas in some illustrative examples.
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