Eigenvalue Normalized Recurrent Neural Networks for Short Term Memory. (arXiv:1911.07964v1 [cs.LG])

Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However, with the eigenvalues of the recurrent matrix on the unit circle, the recurrent state retains all input information which may unnecessarily consume model capacity.…

DLBricks: Composable Benchmark Generation toReduce Deep Learning Benchmarking Effort on CPUs. (arXiv:1911.07967v1 [cs.LG])

The past few years have seen a surge of applying Deep Learning (DL) models for a wide array of tasks such as image classification, object detection, machine translation, etc. While DL models provide an opportunity to solve otherwise intractable tasks, their adoption relies on them being optimized to meet latency and resource requirements. Benchmarking is…

Concerning the geometry of stochastic differential equations and stochastic flows. (arXiv:1911.07941v1 [math.PR])

Following Le Jan and Watanabe we define a connection associated with a non-degenrrate diffusion operators. This connection is characterized here and shown to be the Levi-Civita connection for gradient systems. This both explains why such systems have useful properties and allows us to extend these properties to more general systems. Topics described here include: moment…

Inviscid limit of the compressible Navier-Stokes equations for asymptotically isothermal gases. (arXiv:1911.07948v1 [math.AP])

We prove the existence of relative finite-energy vanishing viscosity solutions of the one-dimensional, isentropic Euler equations under the assumption of an asymptotically isothermal pressure law, that is, $p(\rho)/\rho = O(1)$ in the limit $\rho \to \infty$. This solution is obtained as the vanishing viscosity limit of classical solutions of the one-dimensional, isentropic, compressible Navier–Stokes equations.…

Implicit Regularization of Normalization Methods. (arXiv:1911.07956v1 [cs.LG])

Normalization methods such as batch normalization are commonly used in overparametrized models like neural networks. Here, we study the weight normalization (WN) method (Salimans & Kingma, 2016) and a variant called reparametrized projected gradient descent (rPGD) for overparametrized least squares regression and some more general loss functions. WN and rPGD reparametrize the weights with a…

On the breakdown of regular solutions with finite energy for 3D degenerate compressible Navier-Stokes equations. (arXiv:1911.07965v1 [math.AP])

In this paper, the three-dimensional (3D) isentropic compressible Navier-Stokes equations with degenerate viscosities (\textbf{ICND}) is considered in both the whole space and the periodic domain. First, for the corresponding Cauchy problem, when shear and bulk viscosity coefficients are both given as a constant multiple of the density’s power ($\rho^\delta$ with $0<\delta<1$), based on some elaborate…

Local electric field induced spin photocurrent in ReS2. (arXiv:1911.08049v1 [physics.app-ph])

Circular polarized photocurrent is observed near the electrodes on a few-layer ReS2sample at room temperature. For both electrodes, the spatial distribution of the circular polarized photocurrent shows a feature of two wings, with one positive and the other negative. We suggest that this phenomenon arises from the inverse spin Hall effect due to local electric…

The Acceleration and Confinement of Energetic Electrons by a Termination Shock in a Magnetic Trap: An Explanation for Nonthermal Loop-top Sources during Solar Flares. (arXiv:1911.08064v1 [astro-ph.SR])

Nonthermal loop-top sources in solar flares are the most prominent observational signature that suggests energy release and particle acceleration in the solar corona. Although several scenarios for particle acceleration have been proposed, the origin of the loop-top sources remains unclear. Here we present a model that combines a large-scale magnetohydrodynamic simulation of a two-ribbon flare…