Related papers: ATLAS: Interactive and Educational Linear Algebra …
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
Mathematics is a mountain, but students need more than descriptions of the view: they need a trail they can actually walk. This paper presents the Math Teaching Atlas, a framework for mathematical exposition built around route units (single…
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms,…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
Machine learning models are being used extensively in many important areas, but there is no guarantee a model will always perform well or as its developers intended. Understanding the correctness of a model is crucial to prevent potential…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
After Strassen presented the first sub-cubic matrix multiplication algorithm, many Strassen-like algorithms are presented. Most of them with low asymptotic cost have large hidden leading coefficient which are thus impractical. To reduce the…
We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be…
Active learning is a label-efficient approach to train highly effective models while interactively selecting only small subsets of unlabelled data for labelling and training. In "open world" settings, the classes of interest can make up a…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
Developed to alleviate prohibitive labeling costs, active learning (AL) methods aim to reduce label complexity in supervised learning. While recent work has demonstrated the benefit of using AL in combination with large pre-trained language…
Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…
Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the…
Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…
Automatic Text Summarization (ATS), utilizing Natural Language Processing (NLP) algorithms, aims to create concise and accurate summaries, thereby significantly reducing the human effort required in processing large volumes of text. ATS has…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
Active learning (AL) is a prominent technique for reducing the annotation effort required for training machine learning models. Deep learning offers a solution for several essential obstacles to deploying AL in practice but introduces many…
The introduction of the Basic Linear Algebra Subroutine (BLAS) in the 1970s paved the way for different libraries to solve the same problem with an improved approach and hardware. The new BLAS implementation led to High-Performance…
Classification algorithms to mine data stream have been extensively studied in recent years. However, a lot of these algorithms are designed for supervised learning which requires labeled instances. Nevertheless, the labeling of the data is…