Related papers: Single Element Error Correction/ in a Euclidean Di…

We consider the problem of computing the smallest possible distortion for embedding of a given n-point metric space into R^d, where d is fixed (and small). For d=1, it was known that approximating the minimum distortion with a factor better…

The self-attention (SA) mechanism has demonstrated superior performance across various domains, yet it suffers from substantial complexity during both training and inference. The next-generation architecture, aiming at retaining the…

This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation…

We address the problem of unsupervised learning of complex articulated object models from 3D range data. We describe an algorithm whose input is a set of meshes corresponding to different configurations of an articulated object. The…

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost…

We map categorical variables in a function approximation problem into Euclidean spaces, which are the entity embeddings of the categorical variables. The mapping is learned by a neural network during the standard supervised training…

We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…

This proposes a novel ensemble deep learning-based model to accurately classify, detect and localize different defect categories for aggressive pitches and thin resists (High NA applications).In particular, we train RetinaNet models using…

Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the…

Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize…

We initiate the study of metric embeddings with \emph{outliers}. Given some metric space $(X,\rho)$ we wish to find a small set of outlier points $K \subset X$ and either an isometric or a low-distortion embedding of $(X\setminus K,\rho)$…

Determining the three-dimensional structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using "single particle" cryo-electron…

This contribution is the numerically oriented companion article of the work [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on the numerical resolution of the embedded corrector…

A growing need exists for efficient and accurate methods for detecting defects in semiconductor materials and devices. These defects can have a detrimental impact on the efficiency of the manufacturing process, because they cause critical…

Problems on repeated geometric patterns in finite point sets in Euclidean space are extensively studied in the literature of combinatorial and computational geometry. Such problems trace their inspiration to Erd\H{o}s' original work on that…

Error Correcting Output Codes (ECOC) is a successful technique in multi-class classification, which is a core problem in Pattern Recognition and Machine Learning. A major advantage of ECOC over other methods is that the multi- class problem…

A new, iterative algorithm is presented to calculate the Embedded Element Pattern (EEP) tranformation from a set of patterns computed for a uniform antenna port loading (scaled identinty matrix) to a set of those computed for a non-uniform…

Eddy current testing (ECT) is an effective technique in the evaluation of the depth of metal surface defects. However, in practice, the evaluation primarily relies on the experience of an operator and is often carried out by manual…

Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…