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Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific…

Machine Learning · Statistics 2026-03-04 Jin Cui , Boran Zhao , Jiajun Xu , Jiaqi Guo , Shuo Guan , Pengju Ren

We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation of order $\alpha$ and supply it with the fast and oblivious implementation. In particular, we find a condition for the CQ to be admissible and…

Numerical Analysis · Mathematics 2025-04-25 Maria López-Fernández , Łukasz Płociniczak

We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…

Optimization and Control · Mathematics 2018-08-14 Tony Stillfjord

In this paper, we consider the backward problem for fractional in time evolution equations $\partial_t^\alpha u(t)= A u(t)$ with the Caputo derivative of order $0<\alpha \le 1$, where $A$ is a self-adjoint and bounded above operator on a…

Analysis of PDEs · Mathematics 2022-11-30 S. E. Chorfi , L. Maniar , M. Yamamoto

This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…

Numerical Analysis · Mathematics 2025-07-11 Anna Yesypenko , Chao Chen , Per-Gunnar Martinsson

Convolutional neural networks (CNNs) have a large number of variables and hence suffer from a complexity problem for their implementation. Different methods and techniques have developed to alleviate the problem of CNN's complexity, such as…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Kamran Chitsaz , Mohsen Hajabdollahi , Nader Karimi , Shadrokh Samavi , Shahram Shirani

This paper considers a convolutional neural network transformation that reduces computation complexity and thus speedups neural network processing. Usage of convolutional neural networks (CNN) is the standard approach to image recognition…

Computer Vision and Pattern Recognition · Computer Science 2020-02-19 Elena Limonova , Alexander Sheshkus , Dmitry Nikolaev

Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…

Computation · Statistics 2019-01-23 Zhou Tang , Zhangsheng Yu , Cheng Wang

Convolutional networks (ConvNets) have become a popular approach to computer vision. It is important to accelerate ConvNet training, which is computationally costly. We propose a novel parallel algorithm based on decomposition into a set of…

Neural and Evolutionary Computing · Computer Science 2016-06-21 Aleksandar Zlateski , Kisuk Lee , H. Sebastian Seung

The subdiffusion equation with a Caputo fractional derivative of order $\alpha\in(0,1)$ in time arises in a wide variety of practical applications, and it is often adopted to model anomalous subdiffusion processes in heterogeneous media.…

Numerical Analysis · Mathematics 2015-01-05 Bangti Jin , Raytcho Lazarov , Zhi Zhou

Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…

Computer Vision and Pattern Recognition · Computer Science 2018-11-07 Pravin Nair , Kunal. N. Chaudhury

We present a fast convolution-based technique for computing an approximate, signed Euclidean distance function $S$ on a set of 2D and 3D grid locations. Instead of solving the non-linear, static Hamilton-Jacobi equation ($\|\nabla S\|=1$),…

Computer Vision and Pattern Recognition · Computer Science 2015-02-10 Karthik S. Gurumoorthy , Anand Rangarajan

A novel H3N3-2$_\sigma$ interpolation approximation for the Caputo fractional derivative of order $\alpha\in(1,2)$ is derived in this paper, which improves the popular L2C formula with (3-$\alpha$)-order accuracy. By an interpolation…

Numerical Analysis · Mathematics 2024-02-01 Rui-lian Du , Changpin Li , Zhi-zhong Sun

The widespread use of quantile regression methods depends crucially on the existence of fast algorithms. Despite numerous algorithmic improvements, the computation time is still non-negligible because researchers often estimate many…

Econometrics · Economics 2020-04-08 Victor Chernozhukov , Iván Fernández-Val , Blaise Melly

In this paper we present a method to solve initial value problems for fractional growth models, such as generalizations of the exponential and logistic with periodic harvesting models. Using a discretization of the Caputo derivative we…

Neural and Evolutionary Computing · Computer Science 2025-11-24 Juan Carlos Najera-Tinoco , Martin P. Arciga-Alejandre , Jorge Sanchez-Ortiz , Francisco J. Ariza-Hernandez

Modern approaches for semantic segmentation usually employ dilated convolutions in the backbone to extract high-resolution feature maps, which brings heavy computation complexity and memory footprint. To replace the time and memory…

Computer Vision and Pattern Recognition · Computer Science 2019-03-29 Huikai Wu , Junge Zhang , Kaiqi Huang , Kongming Liang , Yizhou Yu

This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…

Numerical Analysis · Mathematics 2023-03-06 F. Ghoreishi , R. Ghaffari

The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…

Optimization and Control · Mathematics 2021-10-20 Robin Francis , Sundeep Prabhakar Chepuri

A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…

Optimization and Control · Mathematics 2021-09-28 Masoud Ahookhosh , Yurii Nesterov

Deep Convolutional Neural Networks (CNNs) are widely employed in modern computer vision algorithms, where the input image is convolved iteratively by many kernels to extract the knowledge behind it. However, with the depth of convolutional…

Computer Vision and Pattern Recognition · Computer Science 2018-04-11 Chih-Ting Liu , Yi-Heng Wu , Yu-Sheng Lin , Shao-Yi Chien