Variational Dropout and the Local Reparameterization Trick

We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments

Broad Absorption Line Variability in Radio-Loud Quasars

We investigate C IV broad absorption line (BAL) variability within a sample of 46 radio-loud quasars (RLQs), selected from SDSS/FIRST data to include both core-dominated (39) and lobe-dominated (7) objects. The sample consists primarily of high-ionization BAL quasars, and a substantial fraction have large BAL velocities or equivalent widths; their radio luminosities and radio-loudness values span ~2.5 orders of magnitude. We have obtained 34 new Hobby-Eberly Telescope (HET) spectra of 28 BAL RLQs to compare to earlier SDSS data, and we also incorporate archival coverage (primarily dual-epoch SDSS) for a total set of 78 pairs of equivalent width measurements for 46 BAL RLQs, probing rest-frame timescales of ~80-6000 d (median 500 d). In general, only modest changes in the depths of segments of absorption troughs are observed, akin to those seen in prior studies of BAL RQQs. Also similar to previous findings for RQQs, the RLQs studied here are more likely to display BAL variability on longer rest-frame timescales. However, typical values of |Delta_EW| and |Delta_EW|/ are about 40+/-20% lower for BAL RLQs when compared with those of a timescale-matched sample of BAL RQQs. Optical continuum variability is of similar amplitude in BAL RLQs and BAL RQQs; for both RLQs and RQQs, continuum variability tends to be stronger on longer timescales. BAL variability in RLQs does not obviously depend upon their radio luminosities or radio-loudness values, but we do find tentative evidence for greater fractional BAL variability within lobe-dominated RLQs. Enhanced BAL variability within more edge-on (lobe-dominated) RLQs supports some geometrical dependence to the outflow structure.Comment: 27 pages, 16 figures, 6 tables, accepted to MNRAS, full Appendix A at http://www.macalester.edu/~bmille13/balrlqs.htm

The 2+1 Kepler Problem and Its Quantization

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.Comment: 59 pages, LaTeX2e, 9 eps figure

(2+1)-Gravity Solutions with Spinning Particles

We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in the particles' velocities in the dynamic two-body case. A natural boundary for the existence of our gauge choice is provided by some ``CTC horizons'' encircling the particles, within which closed timelike curves occur.Comment: 30 pages, LaTeX, no figure

Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity, namely, short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning, and may serve as substrates for neural systems manipulating temporal information on relevant time scales. The present study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks (CANNs) and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors-the network that is initially being stimulated to an active state decays to a silent state very slowly on the time scale of STD rather than on the time scale of neural signaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.Comment: 40 pages, 17 figure

Functional integration for Regge gravity

A summary is given of recent exact results concerning the functional integration measure in Regge gravity.Comment: 9 pages, AMSLaTex file; talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 September 199