Related papers: ATLAS: Interactive and Educational Linear Algebra …

Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…

Large language models have shown impressive few-shot results on a wide range of tasks. However, when knowledge is key for such results, as is the case for tasks such as question answering and fact checking, massive parameter counts to store…

This is the second installment of an exposition of an ACL2 formalization of elementary linear algebra. It extends the results of Part I, which covers the algebra of matrices over a commutative ring, but focuses on aspects of the theory that…

Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…

Information technologies for studying physical-mathematical disciplines on base of mathematical modeling in the computer algebra system Maple are described.

Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…

We propose a novel, fully nonparametric approach for the multi-task learning, the Multi-task Highly Adaptive Lasso (MT-HAL). MT-HAL simultaneously learns features, samples and task associations important for the common model, while imposing…

Efficient data annotation remains a critical challenge in machine learning, particularly for object detection tasks requiring extensive labeled data. Active learning (AL) has emerged as a promising solution to minimize annotation costs by…

We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…

The goals of Learning Analytics (LA) are manifold, among which helping students to understand their academic progress and improving their learning process, which are at the core of our work. To reach this goal, LA relies on educational…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Recent studies have revealed that, beyond conventional accuracy, calibration should also be considered for training modern deep neural networks. To address miscalibration during learning, some methods have explored different penalty…

Recent work on activation and latent steering has demonstrated that modifying internal representations can effectively guide large language models (LLMs) toward improved reasoning and efficiency without additional training. However, most…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…

Recently, network lasso has drawn many attentions due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values etc), and yields sub-optimal…

This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-$\alpha$. ALADIN-$\alpha$ is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction…