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In state-of-the-art deep neural networks, both feature normalization and feature attention have become ubiquitous. % with significant performance improvement shown in a vast amount of tasks. They are usually studied as separate modules,…

As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…

In this article, families of non-linear subdivision schemes are presented that are based on univariate polynomials up to degree three. Theses families of schemes are constructed by using dynamic iterative re-weighed least squares method.…

The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many…

Point clouds produced by 3D scanning are often sparse, non-uniform, and noisy. Recent upsampling approaches aim to generate a dense point set, while achieving both distribution uniformity and proximity-to-surface, and possibly amending…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

We propose a surface fitting method for unstructured 3D point clouds. This method, called DeepFit, incorporates a neural network to learn point-wise weights for weighted least squares polynomial surface fitting. The learned weights act as a…

In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…

We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…

Existing normal estimation methods for point clouds are often less robust to severe noise and complex geometric structures. Also, they usually ignore the contributions of different neighbouring points during normal estimation, which leads…

In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…

Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…

Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…

Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…