检索结果-内蒙古大学图书馆

2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014

作者： Lee, Eun Jee Abbe, Emmanuel Program in Applied and Computational Mathematics Princeton University United States

ISBN: (纸本)9781479980093

In secure multi-party computations (SMC), parties wish to compute a function on their private data without revealing more information about their data than what the function reveals. In this paper, we investigate two Shannontype questions on this problem. We first consider the traditional one-shot model for SMC which does not assume a probabilistic prior on the data. In this model, private communication and randomness are the key enablers to secure computing, and we investigate a notion of randomness cost and capacity. We then move to a probabilistic model for the data, and propose a Shannon model for discrete memoryless SMC. In this model, correlations among data are the key enablers for secure computing, and we investigate a notion of dependency which permits the secure computation of a function. While the models and questions are general, this paper focuses on summation functions and relies on polar code constructions. © 2014 IEEE.

关键词： Random processes

来源：评论

学校读者我要写书评

暂无评论

A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms 2

A Qualitative Study of the Dynamic Behavior for Adaptive Gra...

引用

2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Stanford University United States Program in Applied and Computational Mathematics Princeton University United States Program in Applied and Computational Mathematics Department of Mathematics Princeton University United States

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial convergence, oscillations, and large spikes in the late phase. The sign gradient descent (signGD) flow, which is the limit of Adam when taking the learning rate to 0 while keeping the momentum parameters fixed, is used to explain the fast initial convergence. For the late phase of Adam, three different types of qualitative patterns are observed depending on the choice of the hyper-parameters: oscillations, spikes, and divergence. In particular, Adam converges much smoother and even faster when the values of the two momentum factors are close to each other. This observation is particularly important for scientific computing tasks, for which the training process usually proceeds into the high precision regime. © 2021 C. Ma, L. Wu & W. E.

关键词： Gradient methods

来源：评论

学校读者我要写书评

暂无评论

Faithful recovery of vector valued functions from incomplete data recolorization and art restoration

引用

1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007

作者： Fornasier, Massimo Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

ISBN: (纸本)9783540728221

On March 11, 1944, the famous Eremitani Church in Padua (Italy) was destroyed in an Allied bombing along with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. We have developed an efficient pattern recognition algorithm to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the fragments is only 77 m 2, while the original area was of several hundreds. This means that we can reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Can one estimate how faithful such restoration is? In this paper we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. We introduce two models for the recovery of vector valued functions from incomplete data, with applications to the fresco recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions for the first functional and functional total variation for the second. We establish the relations between these two models. As a byproduct we develop the basis of a theory of fidelity in color recovery, which is a crucial issue in art restoration and

关键词： Vectors

来源：评论

学校读者我要写书评

暂无评论

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

引用

Communications in Theoretical Physics 2014年第6期61卷 703-709页

作者：钱旭宋松和李伟斌 Department of Mathematics and Systems Science National University of Defense Technology Program in Applied and Computational Mathematics Princeton University State Key Laboratory of High Performance Computing National University of Defense Technology

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

关键词： conservative algorithm coupled nonlinear SchrSdinger equation multiply components unstablewave

来源：评论

学校读者我要写书评

暂无评论

On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers 2

On the emergence of simplex symmetry in the final and penult...

引用

2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Weinan, E. Wojtowytsch, Stephan Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

A recent numerical study observed that neural network classifiers enjoy a large degree of symmetry in the penultimate layer. Namely, if h(x) = Af(x) + b where A is a linear map and f is the output of the penultimate layer of the network (after activation), then all data points xi1, . . ., xi,Ni in a class Ci are mapped to a single point yi by f and the points yi are located at the vertices of a regular k − 1-dimensional standard simplex in a high-dimensional Euclidean space. We explain this observation analytically in toy models for highly expressive deep neural networks. In complementary examples, we demonstrate rigorously that even the final output of the classifier h is not uniform over data samples from a class Ci if h is a shallow network (or if the deeper layers do not bring the data samples into a convenient geometric configuration). © 2021 W. E & S. Wojtowytsch.

关键词： Deep neural networks

来源：评论

学校读者我要写书评

暂无评论

Some observations on high-dimensional partial differential equations with Barron data 2

Some observations on high-dimensional partial differential e...

引用

2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Weinan, E. Wojtowytsch, Stephan Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such function spaces. Consequently, these solutions can be represented efficiently using artificial neural networks, even in high dimension. Conversely, we present examples in which the solution fails to lie in the function space associated to a neural network under consideration. © 2021 W. E & S. Wojtowytsch.

关键词： Partial differential equations

来源：评论

学校读者我要写书评

暂无评论

Variational Boundary Conditions for Molecular Dynamics Simulations of Solids at Low Temperature

引用

Communications in computational Physics 2006年第1期1卷 135-175页

作者： Xiantao Li Weinan E Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA Department of Mathematics&Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA

Boundary conditions for molecular dynamics simulation of crystalline solids are considered with the objective of eliminating the reflection of phonons.A variational formalism is presented to construct boundary conditions that minimize total phonon *** boundary conditions that involve a few neighbors of the boundary atoms and limited number of time steps are found using the variational *** effects are studied and compared with other boundary conditions such as truncated exact boundary conditions or by appending border atoms where artificial damping forces are *** general it is found that,with the same cost or complexity,the variational boundary conditions perform much better than the truncated exact boundary conditions or by appending border atoms with empirical damping *** issues of implementation are discussed for real *** to brittle fracture dynamics is illustrated.

关键词： Boundary condition molecular dynamics phonon reflection crack propagation

来源：评论

学校读者我要写书评

暂无评论

Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday

引用

Science China mathematics 2018年第10期61卷 1733-1740页

作者： Weinan E Qingcan Wang Department of Mathematics and PACM Princeton University Princeton NJ 08544 USA Center for Big Data Research Peking University Beijing 100871 China Beijing Institute of Big Data Research Beijing 100871 China Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.

关键词： neural networks approximation theory analytic functions

来源：评论

学校读者我要写书评

暂无评论

Generalization and Memorization: The Bias Potential Model 2

Generalization and Memorization: The Bias Potential Model

引用

2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Yang, Hongkang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and PACM Princeton University United States

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges. © 2021 H. Yang & W. E.

关键词： Probability distributions

来源：评论

学校读者我要写书评

暂无评论

Accurate Deep Potential model for the Al-Cu-Mg alloy in the full concentration space

引用

Chinese Physics B 2021年第5期30卷 12-19页

作者： Wanrun Jiang Yuzhi Zhang Linfeng Zhang Han Wang Songshan Lake Materials Laboratory Dongguan 523808China Institute of Physics Chinese Academy of SciencesBeijing 100190China Beijing Institute of Big Data Research Beijing 100871China Yuanpei College of Peking University Beijing 100871China Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China

Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface(PES)is the philosopher's stone for unraveling the nature of matter via atomistic *** has been particularly challenging for multi-component alloy systems due to the complex and non-linear nature of the associated *** this work,we develop an accurate PES model for the Al-Cu-Mg system by employing deep potential(DP),a neural network based representation of the PES,and DP generator(DP-GEN),a concurrent-learning scheme that generates a compact set of ab initio data for *** resulting DP model gives predictions consistent with first-principles calculations for various binary and ternary systems on their fundamental energetic and mechanical properties,including formation energy,equilibrium volume,equation of state,interstitial energy,vacancy and surface formation energy,as well as elastic *** benchmark shows that the DP model is ready and will be useful for atomistic modeling of the Al-Cu-Mg system within the full range of concentration.

关键词： potential energy surface deep learning Al-Cu-Mg alloy materials simulation

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：