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Make 1 regularization effective in training sparse CNN

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arXiv 2018年

作者： He, Juncai Jia, Xiaodong Xu, Jinchao Zhang, Lian Zhao, Liang Department of Mathematics Pennsylvania State University University ParkPA16802 United States Department of Computer Science and Engineering Pennsylvania State University University ParkPA16802 United States State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing100190 China

Compressed Sensing using 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. Following Xiao (2010), We first demonstrate that the commonly used stochastic gradient decent (SGD) and variants training algorithm is not an appropriate match with 1 regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA) method. The RDA method of Xiao (2010) 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 1 regularization to achieve a state-of-the-art sparsity for the highly non-convex CNN compared to other weight pruning methods without compromising accuracy (achieving 95% sparsity for ResNet-18 on CIFAR-10, for example). Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Improvements in continuum modeling for biomolecular systems

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Chinese Physics B 2016年第1期25卷 333-338页

作者：乔瑜卢本卓 State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.

关键词： Poisson-Boltzmann equation Poisson-Nernst-Planck equations ionic size effects density func-tional theory

A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem

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arXiv 2017年

作者： Diao, Rui Liu, Ya-Feng Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals {[ai,1, ai,2]}ni=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard. Then, we propose a new fully polynomial time approximation scheme (FPTAS) for solving the general ISSP problem. The time and space complexities of the proposed scheme are O (n max {1/ǫ, log n}) and O (n + 1/ǫ), respectively, where ǫ is the relative approximation error. To the best of our knowledge, the proposed scheme has almost the same time complexity but a significantly lower space complexity compared to the best known scheme. Both the correctness and efficiency of the proposed scheme are validated by numerical simulations. In particular, the proposed scheme successfully solves ISSP instances with n = 100, 000 and ǫ = 0.1% within one second. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity

Two-scale sparse finite element approximations

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Science China Mathematics 2016年第4期59卷 789-808页

作者： LIU Fang ZHU JinWei School of Statistics and Mathematics Central University of Finance and Economics The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and ScientificEngineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general *** any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper *** applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.

关键词： combination discretization eigenvalue finite element postprocessing two-scale

BigNeuron: a resource to benchmark and predict performance of algorithms for automated tracing of neurons in light microscopy datasets

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Nature methods 2023年第6期20卷 824-835页

作者： Linus Manubens-Gil Zhi Zhou Hanbo Chen Arvind Ramanathan Xiaoxiao Liu Yufeng Liu Alessandro Bria Todd Gillette Zongcai Ruan Jian Yang Miroslav Radojević Ting Zhao Li Cheng Lei Qu Siqi Liu Kristofer E Bouchard Lin Gu Weidong Cai Shuiwang Ji Badrinath Roysam Ching-Wei Wang Hongchuan Yu Amos Sironi Daniel Maxim Iascone Jie Zhou Erhan Bas Eduardo Conde-Sousa Paulo Aguiar Xiang Li Yujie Li Sumit Nanda Yuan Wang Leila Muresan Pascal Fua Bing Ye Hai-Yan He Jochen F Staiger Manuel Peter Daniel N Cox Michel Simonneau Marcel Oberlaender Gregory Jefferis Kei Ito Paloma Gonzalez-Bellido Jinhyun Kim Edwin Rubel Hollis T Cline Hongkui Zeng Aljoscha Nern Ann-Shyn Chiang Jianhua Yao Jane Roskams Rick Livesey Janine Stevens Tianming Liu Chinh Dang Yike Guo Ning Zhong Georgia Tourassi Sean Hill Michael Hawrylycz Christof Koch Erik Meijering Giorgio A Ascoli Hanchuan Peng Institute for Brain and Intelligence Southeast University Nanjing China. Microsoft Corporation Redmond WA USA. Tencent AI Lab Bellevue WA USA. Computing Environment and Life Sciences Directorate Argonne National Laboratory Lemont IL USA. Kaya Medical Seattle WA USA. University of Cassino and Southern Lazio Cassino Italy. Center for Neural Informatics Structures and Plasticity Krasnow Institute for Advanced Study George Mason University Fairfax VA USA. Faculty of Information Technology Beijing University of Technology Beijing China. Beijing International Collaboration Base on Brain Informatics and Wisdom Services Beijing China. Nuctech Netherlands Rotterdam the Netherlands. Janelia Research Campus Howard Hughes Medical Institute Ashburn VA USA. Department of Electrical and Computer Engineering University of Alberta Edmonton Alberta Canada. Ministry of Education Key Laboratory of Intelligent Computation and Signal Processing Anhui University Hefei China. Paige AI New York NY USA. Scientific Data Division and Biological Systems and Engineering Division Lawrence Berkeley National Lab Berkeley CA USA. Helen Wills Neuroscience Institute and Redwood Center for Theoretical Neuroscience UC Berkeley Berkeley CA USA. RIKEN AIP Tokyo Japan. Research Center for Advanced Science and Technology (RCAST) The University of Tokyo Tokyo Japan. School of Computer Science University of Sydney Sydney New South Wales Australia. Texas A&M University College Station TX USA. Cullen College of Engineering University of Houston Houston TX USA. Graduate Institute of Biomedical Engineering National Taiwan University of Science and Technology Taipei Taiwan. National Centre for Computer Animation Bournemouth University Poole UK. PROPHESEE Paris France. Department of Neuroscience Columbia University New York NY USA. Mortimer B. Zuckerman Mind Brain Behavior Institute Columbia University New York NY USA. Department of Computer Science Northern Illinois Universit

BigNeuron is an open community bench-testing platform with the goal of setting open standards for accurate and fast automatic neuron tracing. We gathered a diverse set of image volumes across several species that is representative of the data obtained in many neuroscience laboratories interested in neuron tracing. Here, we report generated gold standard manual annotations for a subset of the available imaging datasets and quantified tracing quality for 35 automatic tracing algorithms. The goal of generating such a hand-curated diverse dataset is to advance the development of tracing algorithms and enable generalizable benchmarking. Together with image quality features, we pooled the data in an interactive web application that enables users and developers to perform principal component analysis, t-distributed stochastic neighbor embedding, correlation and clustering, visualization of imaging and tracing data, and benchmarking of automatic tracing algorithms in user-defined data subsets. The image quality metrics explain most of the variance in the data, followed by neuromorphological features related to neuron size. We observed that diverse algorithms can provide complementary information to obtain accurate results and developed a method to iteratively combine methods and generate consensus reconstructions. The consensus trees obtained provide estimates of the neuron structure ground truth that typically outperform single algorithms in noisy datasets. However, specific algorithms may outperform the consensus tree strategy in specific imaging conditions. Finally, to aid users in predicting the most accurate automatic tracing results without manual annotations for comparison, we used support vector machine regression to predict reconstruction quality given an image volume and a set of automatic tracings.

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Reshaping the Cathodic Catalyst Layer for Anion Exchange Membrane Fuel Cells: From Heterogeneous Catalysis to Homogeneous Catalysis

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Angewandte Chemie 2020年第8期133卷

作者： Dr. Rong Ren Xiaojiang Wang Dr. Hengquan Chen Dr. Hamish Andrew Miller Dr. Ihtasham Salam Prof. John Robert Varcoe Dr. Liang Wu Dr. Youhu Chen Prof. Hong-Gang Liao Dr. Ershuai Liu Dr. Francesco Bartoli Dr. Francesco Vizza Dr. Qingying Jia Dr. Qinggang He College of Chemical and Biological Engineering Zhejiang University Hangzhou Zhejiang 310027 China Institute of Chemistry of Organometallic Compounds ICCOM-CNR Polo Scientifico Area CNR 50019 Sesto Fiorentino Italy Department of Chemistry University of Surrey Guildford Surrey GU2 7XH UK School of Chemistry and Chemical Engineering and Key Laboratory of Scientific and Engineering Computing of Ministry of Education Shanghai Jiao Tong University Shanghai China State Key Laboratory of Physical Chemistry of Solid Surfaces College of Chemistry and Chemical Engineering Xiamen University Xiamen 361005 P. R. China Department of Chemistry and Chemical Biology Northeastern University Center for Renewable Energy Technology Boston MA 02115 USA Ningbo Research Institute Zhejiang University Ningbo Zhejiang 315100 China

In anion exchange membrane fuel cells, catalytic reactions occur at a well-defined three-phase interface, wherein conventional heterogeneous catalyst layer structures exacerbate problems, such as low catalyst utilization and limited mass transfer. We developed a structural engineering strategy to immobilize a molecular catalyst tetrakis(4-methoxyphenyl)porphyrin cobalt(II) (TMPPCo) on the side chains of an ionomer (polyfluorene, PF) to obtain a composite material (PF-TMPPCo), thereby achieving a homogeneous catalysis environment inside ion-flow channels, with greatly improved mass transfer and turnover frequency as a result of 100 % utilization of the catalyst molecules. The unique structure of the homogeneous catalysis system comprising interconnected nanoreactors exhibits advantages of low overpotential and high fuel-cell power density. This strategy of reshaping of the catalyst layer structure may serve as a new platform for applications of many molecular catalysts in fuel cells.

关键词： anion exchange membrane fuel cell cathodic catalyst layer homogeneous catalysis oxygen reduction reaction

A lattice Boltzmann model for two-phase flow in porous media

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arXiv 2018年

作者： Chai, Zhenhua Liang, Hong Du, Rui Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Physics Hangzhou Dianzi University Hangzhou310018 China School of Mathematics Southeast University Nanjing210096 China

In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for velocity are accurate and also have a second-order convergence rate in space. Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems. Copyright © 2018, The Authors. All rights reserved.

关键词： Two phase flow

Structured Quasi-Newton methods for optimization with orthogonality constraints

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arXiv 2018年

作者： Hu, Jiang Jiang, Bo Lin, Lin Wen, Zaiwen Yuan, Yaxiang Beijing International Center for Mathematical Research Peking University China School of Mathematical Sciences Key Laboratory for NSLSCS of Jiangsu Province Nanjing Normal University China Department of Mathematics University of California Berkeley BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In particular, we are interested in applications that the Euclidean Hessian itself consists of a computational cheap part and a significantly expensive part. Our basic idea is to keep these parts of lower computational costs but substitute those parts of higher computational costs by the limited-memory quasi-Newton update. More specically, the part related to Euclidean gradient and the cheaper parts in the Euclidean Hessian are preserved. The initial quasi-Newton matrix is further constructed from a limited-memory Nyström approximation to the expensive part. Consequently, our subproblems approximate the original objective function in the Euclidean space and preserve the orthogonality constraints without performing the so-called vector transports. When the subproblems are solved to sufficient accuracy, both global and local q-superlinear convergence can be established under mild conditions. Preliminary numerical experiments on the linear eigenvalue problem and the electronic structure calculation show the effectiveness of our method compared with the state-of-art algorithms. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball Problem of Large Dimensions

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Journal of the Operations Research Society of China 2016年第2期4卷 167-191页

作者： Ya-Feng Liu Rui Diao Feng Ye Hong-Wei Liu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Applied Mathematics Xidian UniversityXi’an 710071China

In this paper,we consider the problem of computing the smallest enclosing ball(SEB)of a set of m balls in Rn,where the product mn is *** first approximate the non-differentiable SEB problem by its log-exponential aggregation function and then propose a computationally efficient inexact Newton-CG algorithm for the smoothing approximation problem by exploiting its special(approximate)sparsity *** key difference between the proposed inexact Newton-CG algorithm and the classical Newton-CG algorithm is that the gradient and the Hessian-vector product are inexactly computed in the proposed algorithm,which makes it capable of solving the large-scale SEB *** give an adaptive criterion of inexactly computing the gradient/Hessian and establish global convergence of the proposed *** illustrate the efficiency of the proposed algorithm by using the classical Newton-CG algorithm as well as the algorithm from Zhou et al.(Comput Optim Appl 30:147–160,2005)as benchmarks.

关键词： Smallest enclosing ball Smoothing approximation Inexact gradient Inexact Newton-CG algorithm Global convergence