Related papers: Experimental Results regarding multiple Machine Le…

We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions often require the calculation of the gradient and Hessian, however,…

Artificial intelligence has made remarkable progress in handling complex tasks, thanks to advances in hardware acceleration and machine learning algorithms. However, to acquire more accurate outcomes and solve more complex issues,…

Machine learning is a field of computer science that builds algorithms that learn. In many cases, machine learning algorithms are used to recreate a human ability like adding a caption to a photo, driving a car, or playing a game. While the…

The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…

Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…

This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…

This paper introduces Quaternion Approximate Networks (QUAN), a novel deep learning framework that leverages quaternion algebra for rotation equivariant image classification and object detection. Unlike conventional quaternion neural…

This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a…

This paper investigates various methods of representing 3D rotations and their impact on the learning process of deep neural networks. We evaluated the performance of ResNet18 networks for 3D rotation estimation using several rotation…

Quantum machine learning deals with leveraging quantum theory with classic machine learning algorithms. Current research efforts study the advantages of using quantum mechanics or quantum information theory to accelerate learning time or…

Deep learning is a research hot topic in the field of machine learning. Real-value neural networks (Real NNs), especially deep real networks (DRNs), have been widely used in many research fields. In recent years, the deep complex networks…

The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…

Over the past century, a correlation has been an essential mathematical technique utilized in engineering sciences, including practically every signal/image processing field. This paper describes an effective method of calculating the…

We study the benefit of sharing representations among tasks to enable the effective use of deep neural networks in Multi-Task Reinforcement Learning. We leverage the assumption that learning from different tasks, sharing common properties,…

Quantum machine learning is receiving significant attention currently, but its usefulness in comparison to classical machine learning techniques for practical applications remains unclear. However, there are indications that certain quantum…

The benefit of multi-task learning over single-task learning relies on the ability to use relations across tasks to improve performance on any single task. While sharing representations is an important mechanism to share information across…

In this article, we give the most genaral form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study on various properties and applications. Firstly we present the definiton,…

Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on Fast Fourier Transform (FFT), they for instance multiply two polynomials…

Meta-learning, or "learning to learn," is a subfield of machine learning where the goal is to develop models and algorithms that can learn from various tasks and improve their learning process over time. Unlike traditional machine learning…