7,142 research outputs found
The wave nature of continuous gravitational waves from microlensing
Gravitational wave predicted by General Relativity is the transverse wave of
spatial strain. Several gravitational waveform signals from binary black holes
and from a binary neutron star system accompanied by electromagnetic
counterparts have been recorded by advanced LIGO and advanced Virgo. In analogy
to light, the spatial fringes of diffraction and interference should also exist
as the important features of gravitational waves. We propose that observational
detection of such fringes could be achieved through gravitational lensing of
continuous gravitational waves. The lenses would play the role of the
diffraction barriers. Considering peculiar motions of the observer, the lens
and the source, the spatial amplitude variation of diffraction or interference
fringes should be detectable as an amplitude modulation of monochromatic
gravitational signal.Comment: Accepted for publication in The Astrophysical Journa
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
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