arXiv subjects

Xiaodong Jia

Publications and source records attributed to Xiaodong Jia.

25 records · Page 2Linked to original sources

arXiv2020

Make $\ell_1$ Regularization Effective in Training Sparse CNN

Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how to make it work. We first demonstrate that the commonly used stochastic gradient decent (SGD) and variants training algorithm is not an appropriate match with $\ell_1$ regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA) method. RDA was originally designed specifically for convex problem, but with new theoretical insight and algorithmic modifications (using proper initialization and adaptivity), we have made it an effective match with $\ell_1$ regularization to achieve a state-of-the-art sparsity for CNN compared to other weight pruning methods without compromising accuracy (achieving 95\% sparsity for ResNet18 on CIFAR-10, for example).

cs.LG↗

arXiv2020

Completing Simple Valuations in K-categories

We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a monad Kc o Vs on each K-category A. We also characterize the Eilenberg-Moore algebras of Kc o Vs as the weakly locally convex K-cones, and its algebra morphisms as the continuous linear maps. In addition, we explicitly describe the distributive law of Vs over Kc, which allows us to show that the K-completion of any locally convex (respectively, weakly locally convex, locally linear) topological cone is a locally convex (respectively, weakly locally convex, locally linear) K-cone. We also give an example - the Cantor tree with a top - that shows the dcpo-completion of the simple valuations is not the D-completion of the simple valuations in general, where D is the category of monotone convergence spaces and continuous maps.

cs.LO↗

arXiv2019

Core-compactness of Smyth powerspaces

We prove that the Smyth powerspace Q(X) of a topological space X is core-compact if and only if X is locally compact. As a straightforward consequence we obtain that the Smyth powerspace construction does not preserve core-compactness generally.

math.GN↗

arXiv2019

Algebras of the extended probabilistic powerdomain monad

We investigate the Eilenberg-Moore algebras of the extended probabilistic powerdomain monad $\mathcal V_w$ over the category $\mathbf{TOP}_0$ of $T_0$ topological spaces and continuous maps. We prove that every $\mathcal V_w$-algebra in our setting is a weakly locally convex sober topological cone, and that a map is the structure map of a $\mathcal V_w$-algebra if and only if it is continuous and sends every continuous valuation to its unique barycentre. Conversely, for locally linear sober cones (a strong form of local convexity), the mere existence of barycentres entails that the barycentre map is the structure map of a $\mathcal V_w$-algebra; moreover the algebra morphisms are exactly the linear continuous maps in that case. We also examine the algebras of two related monads, the simple valuation monad $\mathcal V_{\mathrm f}$ and the point-continuous valuation monad $\mathcal V_{\mathrm p}$. In $\mathbf{TOP}_0$ their algebras are fully characterised as weakly locally convex topological cones and weakly locally convex sober topological cones, respectively. In both cases, the algebra morphisms are continuous linear maps between the corresponding algebras.

math.GN↗

arXiv2019

Domain-complete and LCS-complete spaces

We study $G_δ$ subspaces of continuous dcpos, which we call domain-complete spaces, and $G_δ$ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in particular, all continuous dcpos-, all topologically complete spaces in the sense of Čech, and all quasi-Polish spaces-in particular, all Polish spaces. We show that LCS-complete spaces are sober, Wilker, compactly Choquet-complete, completely Baire, and $\odot$-consonant-in particular, consonant; that the countably-based LCS-complete (resp., domain-complete) spaces are the quasi-Polish spaces exactly; and that the metrizable LCS-complete (resp., domain-complete) spaces are the completely metrizable spaces. We include two applications: on LCS-complete spaces, all continuous valuations extend to measures, and sublinear previsions form a space homeomorphic to the convex Hoare powerdomain of the space of continuous valuations.

math.GN↗

arXiv2018

A simplified convolutional sparse filter for impulsive signature enhancement and its application to the prognostic of rotating machinery

Impulsive signature enhancement (ISE) is an important topic in the monitoring of rotating machinery and many different methods have been proposed. Even though, the topic of how to leverage these ISE techniques to improve the data quality in terms of prognostics and health management (PHM) still needs to be investigated. In this work, a systematic view for data quality enhancement is presented. The data quality issues for the prognostics and health management (PHM) of rotating machinery are identified, and the major steps to enhance data quality are organized. Based on this, a novel ISE algorithm is originally proposed, the importance of extracting scale invariant features are explained, and also related features are proposed for the PHM of rotating machinery. In order to demonstrate the effectiveness of the novelties, two experimental studies are presented. The final results indicate that the proposed method can be effectively employed to enhance the data quality for machine failure detection and diagnosis.

stat.AP↗

arXiv2014

Long-range micro-pulse aerosol lidar at 1.5 um with an up-conversion single-photon detector

A micro-pulse lidar at eye-safe wavelength is constructed based on an up-conversion single-photon detector. The ultralow noise detector enables using integration technique to improve the signal-to-noise ratio of the atmospheric backscattering even at daytime. With the pulse energy of 110uJ, the pulse repetition rate of 15 kHz, the optical antenna diameter of 100 mm and integration time of 5 minutes, a horizontal detection range of 7 km is realized. In the demonstration experiment, atmospheric visibility over 24 hours is monitored continuously, with results in accordance with the weather forecasts.

physics.optics↗