Related papers: Quaternion Backpropagation
This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…
Recently, the connectionist temporal classification (CTC) model coupled with recurrent (RNN) or convolutional neural networks (CNN), made it easier to train speech recognition systems in an end-to-end fashion. However in real-valued models,…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
The backpropagation algorithm, which had been originally introduced in the 1970s, is the workhorse of learning in neural networks. This backpropagation algorithm makes use of the famous machine learning algorithm known as Gradient Descent,…
Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate…
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…
We describe an approximation to backpropagation algorithm for training deep neural networks, which is designed to work with synapses implemented with memristors. The key idea is to represent the values of both the input signal and the…
Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for…
This paper introduces a novel idea for representation of individuals using quaternions in swarm intelligence and evolutionary algorithms. Quaternions are a number system, which extends complex numbers. They are successfully applied to…
In recent years, an increasing number of neural network models have included derivatives with respect to inputs in their loss functions, resulting in so-called double backpropagation for first-order optimization. However, so far no general…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…
We investigate the use of derivative information for Batch Active Learning in Gaussian Process regression models. The proposed approach employs the predictive covariance matrix for selection of data batches to exploit full correlation of…
Working in a semi-constructive logical system that supports the extraction of concurrent programs, we extract a program inverting non-singular real valued matrices from a constructive proof based on Gaussian elimination. Concurrency is used…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…