48,127 research outputs found
Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains
We consider the minimization of an objective function given access to
unbiased estimates of its gradient through stochastic gradient descent (SGD)
with constant step-size. While the detailed analysis was only performed for
quadratic functions, we provide an explicit asymptotic expansion of the moments
of the averaged SGD iterates that outlines the dependence on initial
conditions, the effect of noise and the step-size, as well as the lack of
convergence in the general (non-quadratic) case. For this analysis, we bring
tools from Markov chain theory into the analysis of stochastic gradient. We
then show that Richardson-Romberg extrapolation may be used to get closer to
the global optimum and we show empirical improvements of the new extrapolation
scheme
Preliminary Results on the Empirical Applicability of the Tsallis Distribution in Elastic Hadron Scattering
We show that the proton-proton elastic differential cross section data at dip
position and beyond can be quite well described by a parametrization based on
the Tsallis distribution, with only five free fit parameters. Extrapolation of
the results obtained at 7 TeV to large momentum transfer, suggests that hadrons
may not behave as a black-disk at the asymptotic energy region.Comment: 3 pages, 1 figure, version matching proceedings style, XII Hadron
Physics, 2012, AIP Proc. Con
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