64,549 research outputs found
High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Models
Learning in deep models using Bayesian methods has generated significant
attention recently. This is largely because of the feasibility of modern
Bayesian methods to yield scalable learning and inference, while maintaining a
measure of uncertainty in the model parameters. Stochastic gradient MCMC
algorithms (SG-MCMC) are a family of diffusion-based sampling methods for
large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient
thermostats (mSGNHT) augment each parameter of interest, with a momentum and a
thermostat variable to maintain stationary distributions as target posterior
distributions. As the number of variables in a continuous-time diffusion
increases, its numerical approximation error becomes a practical bottleneck, so
better use of a numerical integrator is desirable. To this end, we propose use
of an efficient symmetric splitting integrator in mSGNHT, instead of the
traditional Euler integrator. We demonstrate that the proposed scheme is more
accurate, robust, and converges faster. These properties are demonstrated to be
desirable in Bayesian deep learning. Extensive experiments on two canonical
models and their deep extensions demonstrate that the proposed scheme improves
general Bayesian posterior sampling, particularly for deep models.Comment: AAAI 201
Rotationally symmetric harmonic diffeomorphisms between surfaces
In this paper, we show that the nonexistence of rotationally symmetric
harmonic diffeomorphism between the unit disk without the origin and a
punctured disc with hyperbolic metric on the target.Comment: Minor typos correcte
Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate
We study sequential scattering in superradiance from a Bose-Einstein
condensate pumped by a two-frequency laser beam. We find that the distribution
of atomic side modes presents highly different patterns for various frequency
difference between the two pump components. A novel distribution is observed,
with a frequency difference of eight times the recoil frequency. These
observations reveal that the frequency overlap between the end-fire modes
related to different side modes plays an essential role in the dynamics of
sequential superradiant scattering. The numerical results from a semiclassical
model qualitatively agree with our observations.Comment: Submitted to PR
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