Related papers: LU factorization with panel rank revealing pivotin…

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional…

A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplications, which greatly limits the benefits that…

Intuitively, an ideal collaborative filtering (CF) model should learn from users' full rankings over all items to make optimal top-K recommendations. Due to the absence of such full rankings in practice, most CF models rely on pairwise loss…

Pipeline-parallel distributed optimization is essential for large-scale machine learning but is challenged by significant communication overhead from transmitting high-dimensional activations and gradients between workers. Existing…

A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be…

Link prediction in a graph is the problem of detecting the missing links that would be formed in the near future. Using a graph representation of the data, we can convert the problem of classification to the problem of link prediction which…

Low-latency gravitational wave search pipelines such as GstLAL take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in…

Federated Learning (FL) faces significant challenges related to communication efficiency and performance reduction when scaling to many clients. To address these issues, we explore the potential of using low-rank updates and provide the…

This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining…

The FLAME methodology for deriving linear algebra algorithms from specification, first introduced around 2000, has been successfully applied to a broad cross section of operations. An open question has been whether it can yield algorithms…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including…

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…

We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to…

We present parallel and sequential dense QR factorization algorithms that are both optimal (up to polylogarithmic factors) in the amount of communication they perform, and just as stable as Householder QR. Our first algorithm, Tall Skinny…

The dominant paradigm in modern neural networks relies on simple, monotonically-increasing activation functions like ReLU. While effective, this paradigm necessitates large, massively-parameterized models to approximate complex functions.…

The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…

Ranking documents using Large Language Models (LLMs) by directly feeding the query and candidate documents into the prompt is an interesting and practical problem. However, researchers have found it difficult to outperform fine-tuned…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…