Related papers: Deep Quaternion Networks
Deep learning has recently demonstrated its ability to rival the human brain for visual object recognition. As datasets get larger, a natural question to ask is if existing deep learning architectures can be extended to handle the 50+K…
Convolutional Neural Network (CNN) has gained state-of-the-art results in many pattern recognition and computer vision tasks. However, most of the CNN structures are manually designed by experienced researchers. Therefore, auto- matically…
Transceivers used for telecommunications transmit and receive specific modulation patterns that are represented as sequences of complex numbers. Classifying modulation patterns is challenging because noise and channel impairments affect the…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…
Recent deep-learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This chapter covers recent work aiming to interpret models by attributing…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
In deep learning, mini-batch training is commonly used to optimize network parameters. However, the traditional mini-batch method may not learn the under-represented samples and complex patterns in the data, leading to a longer time for…
Machine learning is making substantial progress in diverse applications. The success is mostly due to advances in deep learning. However, deep learning can make mistakes and its generalization abilities to new tasks are questionable. We ask…
Deep learning has become very popular for tasks such as predictive modeling and pattern recognition in handling big data. Deep learning is a powerful machine learning method that extracts lower level features and feeds them forward for the…
Deep learning and quantum computing have achieved dramatic progresses in recent years. The interplay between these two fast-growing fields gives rise to a new research frontier of quantum machine learning. In this work, we report the first…
Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
Background: It is still an open research area to theoretically understand why Deep Neural Networks (DNNs)---equipped with many more parameters than training data and trained by (stochastic) gradient-based methods---often achieve remarkably…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
The purpose of this paper is to propose a new multi-layer feedforward quaternion neural network model architecture, Reverse Quaternion Neural Network which utilizes the non-commutative nature of quaternion products, and to clarify its…
Deep Learning has demonstrated a significant improvement against traditional machine learning approaches in different domains such as image and speech recognition. Their success on benchmark datasets is transferred to the real-world through…
Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of…