Related papers: Quaternion Product Units for Deep Learning on 3D R…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
In this paper, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with reduced implementation complexities. The first solution: a…
Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic…
Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and…
Recommendation system has been a widely studied task both in academia and industry. Previous works mainly focus on homogeneous recommendation and little progress has been made for heterogeneous recommender systems. However, heterogeneous…
Deep reinforcement learning is an emerging machine learning approach which can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision…
The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be…
With the beginning of the noisy intermediate-scale quantum (NISQ) era, a quantum neural network (QNN) has recently emerged as a solution for several specific problems that classical neural networks cannot solve. Moreover, a quantum…
Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…
Deep Q-learning is investigated as an end-to-end solution to estimate the optimal strategies for acting on time series input. Experiments are conducted on two idealized trading games. 1) Univariate: the only input is a wave-like price time…
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
Combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key…
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,…
Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…
Imitation learning techniques have been used as a way to transfer skills to robots. Among them, dynamic movement primitives (DMPs) have been widely exploited as an effective and an efficient technique to learn and reproduce complex discrete…