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Related papers: L2-Stability Analysis of The Set-Membership Affine…

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In this paper we derive stability estimates in $L^{2}$- and $L^{\infty}$- based Sobolev spaces for the $L^{2}$ projection and a family of quasiinterolants in the space of smooth, 1-periodic, polynomial splines defined on a uniform mesh in…

Numerical Analysis · Mathematics 2021-07-09 D. C. Antonopoulos V. A. Dougalis

Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often…

Machine Learning · Computer Science 2022-08-22 Nisha Chandramoorthy , Andreas Loukas , Khashayar Gatmiry , Stefanie Jegelka

We have performed a series of high resolution N-body experiments on a Connection Machine CM-5 in order to study the stability of collisionless self-gravitating spherical systems. We interpret our results in the framework of symplectic…

Astrophysics · Physics 2015-06-24 J. Perez , J-M Alimi , J-J Aly , H. Scholl

In this paper, we study the L2 stability of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider the case when a small periodic perturbation is applied to a uniform mesh. For this case, we…

Numerical Analysis · Mathematics 2024-08-30 Pavel Bakhvalov , Mikhail Surnachev

Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…

Computer Science and Game Theory · Computer Science 2024-08-20 Kimon Boehmer , Niclas Boehmer

Affine projection algorithm (APA) is a well-known algorithm in adaptive filtering applications such as audio echo cancellation. APA relies on three parameters: $P$ (projection order), $\mu$ (step size) and $\delta$ (regularization…

Information Theory · Computer Science 2023-10-16 Shirin Jalali , Carl Nuzman , Yue Sun

In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of…

Signal Processing · Electrical Eng. & Systems 2018-04-24 Aven Samareh , Mahshid Salemi Parizi

Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These…

Machine Learning · Statistics 2018-04-24 Hunter Lang , David Sontag , Aravindan Vijayaraghavan

This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the…

Optimization and Control · Mathematics 2022-11-10 Xiaowei Li , Xuqi Zhang , Zhiguo Wang , Xiaojing Shen

We prove a general result implying the $L^2$ stability of Haar decompositions of $L^2({\bf R}^d)$ functions when the Haar functions are distorted by arbitrary, independent, affine changes of variable that are close to the identity. We apply…

Classical Analysis and ODEs · Mathematics 2023-07-26 James Michael Wilson

For a nondegenerate analytic system with a conserved quantity, a classic result by Lyapunov guarantees the existence of an analytic manifold of periodic orbits tangent to any two-dimensional, elliptic eigenspace of a fixed point satisfying…

Dynamical Systems · Mathematics 2019-07-16 Rafael de la Llave , Florian Kogelbauer

It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial…

Machine Learning · Computer Science 2023-03-30 Wei Wei , Jiahuan Zhou , Ying Wu

Building object-level maps can facilitate robot-environment interactions (e.g. planning and manipulation), but objects could often have multiple probable poses when viewed from a single vantage point, due to symmetry, occlusion or…

Robotics · Computer Science 2021-09-09 Ziqi Lu , Qiangqiang Huang , Kevin Doherty , John Leonard

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

Optimization and Control · Mathematics 2017-01-03 Dongcai Su

With significant annotation savings, point supervision has been proven effective for numerous 2D and 3D scene understanding problems. This success is primarily attributed to the structured output space; i.e., samples with high spatial…

Computer Vision and Pattern Recognition · Computer Science 2023-04-18 Leiyao Cui , Xiaoxue Chen , Hao Zhao , Guyue Zhou , Yixin Zhu

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is…

Systems and Control · Computer Science 2020-11-06 Francesco Ferrante , Frédéric Gouaisbaut , Ricardo G. Sanfelice , Sophie Tarbouriech

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by their tendency to generate similar outputs…

Machine Learning · Computer Science 2026-05-12 Rania Briq , Michael Kamp , Ohad Fried , Sarel Cohen , Stefan Kesselheim

Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…

Computational Geometry · Computer Science 2014-03-26 Tamal K. Dey , Fengtao Fan , Yusu Wang

In this paper, we propose and prove the theorem regarding the stability of attributes in a decision system. Based on the theorem, we propose the LRA framework for accelerating rough set algorithms. It is a general-purpose framework which…

Artificial Intelligence · Computer Science 2020-11-03 Shuyin Xia , Wenhua Li , Guoyin Wang , Xinbo Gao , Changqing Zhang , Elisabeth Giem

In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal point algorithm which involves multiple parameters. Yao and…

Logic · Mathematics 2021-01-13 Bruno Dinis , Pedro Pinto