Related papers: A Convergence Study for Reduced Rank Extrapolation…

The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

Decision-tree-based ensemble classification methods (DTEMs) are a prevalent tool for supervised anomaly detection. However, due to the continued growth of datasets, DTEMs result in increasing drawbacks such as growing memory footprints,…

In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse…

Existing Reward Models (RMs), typically trained on general preference data, struggle in Retrieval Augmented Generation (RAG) settings, which require judging responses for faithfulness to retrieved context, relevance to the user query,…

This paper investigates the effectiveness of using the Random Projection Ensemble (RPE) approach in Quadratic Discriminant Analysis (QDA) for ultrahigh-dimensional classification problems. Classical methods such as Linear Discriminant…

This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

Sum of Ranking Differences (SRD) is a relatively novel, non-para-metric statistical procedure that has become increasingly popular recently. SRD compares solutions via a reference by applying a rank transformation on the input and…

Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…

The ResNet and its variants have achieved remarkable successes in various computer vision tasks. Despite its success in making gradient flow through building blocks, the simple shortcut connection mechanism limits the ability of…

We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted Gaussian measurements, with no prior knowledge on the intrinsic rank. We consider the robust matrix factorization approach. We employ a robust $\ell_1$…

Relation Extraction (RE) is a crucial task in Information Extraction, which entails predicting relationships between entities within a given sentence. However, extending pre-trained RE models to other languages is challenging, particularly…

Generative relation extraction (RE) commonly involves first reformulating RE as a linguistic modeling problem easily tackled with pre-trained language models (PLM) and then fine-tuning a PLM with supervised cross-entropy loss. Although…

Low-rank tensor decomposition generalizes low-rank matrix approximation and is a powerful technique for discovering low-dimensional structure in high-dimensional data. In this paper, we study Tucker decompositions and use tools from…

Relation extraction (RE) aims to identify relations between entities mentioned in texts. Although large language models (LLMs) have demonstrated impressive in-context learning (ICL) abilities in various tasks, they still suffer from poor…

Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…

We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent partial differential equations (PDEs), where the modes…

Machine learning classification models trained with empirical risk minimization (ERM) often inadvertently rely on spurious correlations. When absent in the test data, these unintended associations between non-target attributes and target…

Among the various machine learning methods solving partial differential equations, the Random Feature Method (RFM) stands out due to its accuracy and efficiency. In this paper, we demonstrate that the approximation error of RFM exhibits…