Related papers: Low-Complexity Quaternion Adaptive Filters

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…

Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…

Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…

A novel adaptive filtering method called $q$-Volterra least mean square ($q$-VLMS) is presented in this paper. The $q$-VLMS is a nonlinear extension of conventional LMS and it is based on Jackson's derivative also known as $q$-calculus. In…

Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by…

Driven by recent advances in artificial intelligence (AI), a growing literature has demonstrated the potential for using large language models (LLMs) as scalable surrogates to generate human-like responses in many business applications. Two…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

Reinforcement learning is a popular machine learning paradigm which can find near optimal solutions to complex problems. Most often, these procedures involve function approximation using neural networks with gradient based updates to…

One of the tasks in color image processing and computer vision is to recover clean data from partial observations corrupted by noise. To this end, robust quaternion matrix completion (QMC) has recently attracted more attention and shown its…

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates continual learning (CL) to update models online, enabling adaptation to new tasks while preserving…

This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…

Reinforcement Learning (RL) algorithms often require long training to become useful, especially in complex environments with sparse rewards. While techniques like reward shaping and curriculum learning exist to accelerate training, these…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive…

The purpose of this note is to discuss some aspects of recently proposed fractional-order variants of complex least mean square (CLMS) and normalized least mean square (NLMS) algorithms in ``Design of Fractional-order Variants of Complex…

We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

As data retrieval demands become increasingly complex, traditional search methods often fall short in addressing nuanced and conceptual queries. Vector similarity search has emerged as a promising technique for finding semantically similar…