A continuous-time analysis of distributed stochastic gradient

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing -- where synchronization between agents is induced through communication with a common signal -- we quantify how synchronization can significantly reduce the magnitude of the noise felt by the individual distributed agents and by their spatial mean. This noise reduction is in turn associated with a reduction in the smoothing of the loss function imposed by the stochastic gradient approximation. Through simulations on model non-convex objectives, we demonstrate that coupling can stabilize higher noise levels and improve convergence. We provide a convergence analysis for strongly convex functions by deriving a bound on the expected deviation of the spatial mean of the agents from the global minimizer for an algorithm based on quorum sensing, the same algorithm with momentum, and the Elastic Averaging SGD (EASGD) algorithm. We discuss extensions to new algorithms which allow each agent to broadcast its current measure of success and shape the collective computation accordingly. We supplement our theoretical analysis with numerical experiments on convolutional neural networks trained on the CIFAR-10 dataset, where we note a surprising regularizing property of EASGD even when applied to the non-distributed case. This observation suggests alternative second-order in-time algorithms for non-distributed optimization that are competitive with momentum methods.Comment: 9/14/19 : Final version, accepted for publication in Neural Computation. 4/7/19 : Significant edits: addition of simulations, deep network results, and revisions throughout. 12/28/18: Initial submissio

Inclusive quasielastic scattering of polarized electrons from polarized nuclei

The inclusive quasielastic response functions that appear in the scattering of polarized electrons from polarized nuclei are computed and analyzed for several closed-shell-minus-one nuclei with special attention paid to 39K. Results are presented using two models for the ejected nucleon --- when described by a distorted wave in the continuum shell model or by a plane wave in PWIA with on- and off-shell nucleons. Relativistic effects in kinematics and in the electromagnetic current have been incorporated throughout. Specifically, the recently obtained expansion of the electromagnetic current in powers only of the struck nucleon's momentum is employed for the on-shell current and the effects of the first-order terms (spin-orbit and convection) are compared with the zeroth-order (charge and magnetization) contributions. The use of polarized inclusive quasielastic electron scattering as a tool for determining near-valence nucleon momentum distributions is discussed.Comment: 51 LaTeX pages, 14 Postscript figure

Role of Long-Range Correlations on the Quenching of Spectroscopic Factors

We consider the proton and neutron quasiparticle orbits around the closed-shell 56Ni and 48Ca isotopes. It is found that large model spaces (beyond the capability of shell-model applications) are necessary for predicting the quenchings of spectroscopic factors. The particle-vibration coupling is identified as the principal mechanism. Additional correlations--due to configuration with several particle-hole excitations--are estimated using shell-model calculations and generate an extra reduction which is < ~4% for most quasiparticle states. The theoretical calculations nicely agree with (e,e'p) and heavy ion knock-out experiments. These results open a new path for a microscopic understanding of the shell-model.Comment: Minor comments added and typos corrected. Accepted for publication on Phys. Rev. Let

Proton Electromagnetic Form Factor Ratios at Low Q^2

We study the ratio $R\equiv\mu G_E(Q^2)/G_M(Q^2)$ of the proton at very small values of $Q^2$. Radii commonly associated with these form factors are not moments of charge or magnetization densities. We show that the form factor $F_2$ is correctly interpretable as the two-dimensional Fourier transformation of a magnetization density. A relationship between the measurable ratio and moments of true charge and magnetization densities is derived. We find that existing measurements show that the magnetization density extends further than the charge density, in contrast with expectations based on the measured reduction of $R$ as $Q^2$ increases.Comment: 4 pages 3 figures We have corrected references, figures and some typographical error

Density dependence of resonance broadening and shadowing effects in nuclear photoabsorption

Medium effects as a function of the mass number $A$ are studied in the total photonuclear cross section from the $\Delta$-resonance region up to the region where shadowing effects are known to exist. A consistent picture is obtained by simply assuming a density dependence of the different mechanisms of resonance broadening and shadowing. The $\Delta$-mass shift is found to increase with $A$.Comment: 7 pages, LaTeX, 2 figures available from the author

Initial and Final State Interaction Effects in Small-x Quark Distributions

We study the initial and final state interaction effects in the transverse momentum dependent parton distributions in the small-$x$ saturation region. In particular, we discuss the quark distributions in the semi-inclusive deep inelastic scattering, Drell-Yan lepton pair production and dijet-correlation processes in $pA$ collisions. We calculate the quark distributions in the scalar-QED model and then extend to the color glass condensate formalism in QCD. The quark distributions are found universal between the DIS and Drell-Yan processes. On the other hand, the quark distribution from the $qq'\to qq'$ channel contribution to the dijet-correlation process is not universal. However, we find that it can be related to the quark distribution in DIS process by a convolution with the normalized unintegrated gluon distribution in the color glass condensate formalism in the large $N_c$ limit.Comment: 20 pages, 6 figure

Transverse-momentum distributions in a diquark spectator model

All the leading-twist parton distribution functions are calculated in a spectator model of the nucleon, using scalar and axial-vector diquarks. Single gluon rescattering is used to generate T-odd distribution functions. Different choices for the diquark polarization states are considered, as well as a few options for the form factor at the nucleon-quark-diquark vertex. The results are listed in analytic form and interpreted in terms of light-cone wave functions. The model parameters are fixed by reproducing the phenomenological parametrization of unpolarized and helicity parton distributions at the lowest available scale. Predictions for the other parton densities are given and, whenever possible, compared with available phenomenological parametrizations.Comment: 42 pages, 13 figures in .eps format. RevTeX style. Minor typos corrected, added one referenc

Inclusive (e,e′N)(e,e^\prime N), (e,e′NN)(e,e^\prime NN), (e,e′π)(e,e^\prime \pi) ... reactions in nuclei

We study the inclusive $(e,e^\prime N)$, $(e,e^\prime NN)$, $(e,e^\prime \pi)$, $(e,e^\prime \pi N)$ reactions in nuclei using a Monte Carlo simulation method to treat the multichannel problem of the final state. The input consists of reaction probabilities for the different steps evaluated using microscopical many body methods. We obtain a good agreement with experiment in some channels where there is data and make predictions for other channels which are presently under investigation in several electron laboratories. The comparison of the theoretical results with experiment for several kinematical conditions and diverse channels can serve to learn about different physical processes ocurring in the reaction. The potential of this theoretical tool to make prospections for possible experiments, aiming at pinning down certain reaction probabilities, is also emphasized.Comment: 21 pages (LaTeX + figure files

Analysis of Meson Exchange and Isobar Currents in (e,e'p) Reactions from O-16

An analysis of the effects of meson exchange and isobar currents in exclusive (e,e'p) processes from O-16 under quasi-free kinematics is presented. A model that has probed its feasibility for inclusive quasi-elastic (e,e') processes is considered. Sensitivity to final state interactions between the outgoing proton and the residual nucleus is discussed by comparing the results obtained with phenomenological optical potentials and a continuum nuclear shell-model calculation. The contribution of the meson-exchange and isobar currents to the response functions is evaluated and compared to previous calculations, which differ notably from our results. These two-body contributions cannot solve the puzzle of the simultaneous description of the different responses experimentally separated. Copyright 1999 by The American Physical SocietyComment: 5 pages, plus 3 PS figures. To be published in Phys. Rev. C Updated figure