Related papers: Matrix diagonalization and singular value decompos…
Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are…
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in…
Programming students have a widespread access to powerful Generative AI tools like ChatGPT. While this can help understand the learning material and assist with exercises, educators are voicing more and more concerns about an overreliance…
While Large Language Models (LLMs) excel at the Winograd Schema Challenge (WSC), a coreference resolution task testing common-sense reasoning through pronoun disambiguation, they struggle with instances that feature minor alterations or…
Repeating a gate sequence multiple times amplifies systematic errors coherently, making it a useful tool for characterizing quantum gates. However, the precision of such an approach is limited by low-frequency noises, while its efficiency…
Tabled evaluation is a recognized and powerful technique that overcomes some limitations of traditional Prolog systems in dealing with recursion and redundant sub-computations. We can distinguish two main categories of tabling mechanisms:…
Value decomposition is a central approach in multi-agent reinforcement learning (MARL), enabling centralized training with decentralized execution by factorizing the global value function into local values. To ensure individual-global-max…
Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
While transfer learning is an effective strategy, it often overlooks the opportunity to leverage knowledge from numerous available models online. Addressing this multi-source transfer learning problem is a promising path to boost…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
Face Recognition Systems (FRS) are increasingly vulnerable to face-morphing attacks, prompting the development of Morphing Attack Detection (MAD) algorithms. However, a key challenge in MAD lies in its limited generalizability to unseen…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…