Investigations in quantum inspired neural network learning algorithms

Abstract

Arti cial Neural Network (ANN) is one of the most popular and promising areas of research in arti cial intelligence. ANN has been widely used for the classi cation task due to its characteristic of massive parallelism, learning ability, generalization ability, and fault tolerance. For solving classi cation task, many models have been used like Backpropagation, Perceptron, Recurrent Neural Network and these models have been successfully applied in several elds like economics, defense, stock market, engineering, and medical. The neural network is formed using several learning parameters like connection weights, the threshold of the neuron, number of layers, number of hidden layer neurons. Finding optimal classi cation results need the optimal value of these learning parameters. Several training techniques have been proposed to nd the optimal valueof these parameters within di erent neural network architectures. However, it is still an open area of research to nd the optimal value of neural network parameters. The evolutionary algorithms like genetic algorithm, particle swarm optimization, ant colony optimization are also used by many researchers to nd the optimal value of neural network learning parameters. Recently the quantum evolutionary algorithm (QEA) has been applied to many classi cation problems and producing very promising results. QEA is a population-based probabilistic EA that integrates concepts from quantum computing for higher representation power and robust search. QEAs are characterized by population dynamics, individual representation, and evaluation function. Initially, QEA can represent diverse individuals probabilistically because a quantum bit (Q) individual ismade up of several qubits (q) represents the linear superposition of all possible states with the same probability. The observation process used here gives a large search space to nd the optimal value of required parameter. The quantum rotational gate provide exploitation to restrict the algorithm to stuck withthe problem of local minima and maxima. We proposed neural network architecture using quantum computing concept. The connection weights are evolved rst using evolutionary quantum computing concept and neural network is formed constructively by adding neurons in the hidden layer one by one. However, the threshold of neurons has been decided manually which may lead solution to local minima and maxima problem. Therefore the work has been extended by evolving threshold of neuron along with connection weights. Finding a range of search space is also an important issue. Therefore, to evolve threshold of neuron optimally, the existing work is enhanced and threshold boundary parameter is proposed. The algorithm has been used to classify o ine signature dataset. For complex datasets, having noisy samples there are chances of overlapping in samples from multiple classes. In order to handle such problem, a neural network architecture using quantum and fuzzy concept has been proposed for two-class dataset having overlapped samples. The fuzzy concept has been usedto evolve connection weight or learning of neural network whereas the fuzzy algorithm is optimized using evolutionary quantum computing concept. The fuzzi er parameter which decided overlapping between clusters has been evolved using evolutionary quantum computing concept. The fuzzy concept has one more parameter that is cluster centroids, which is generally initialized randomly. This work has been extended by proposing a quantum-inspired fuzzy based neural network learning algorithm for multi-class dataset having overlapped samples. In this, along with fuzzi er parameter, the cluster centroids which act as connection weights in the neural network are being evolved using quantum computing concept. To deal with complex dataset like image dataset, web dataset, face reorganization object identi cation, and speech reorganization, deep neural network are proposed. However, the learning algorithm of deep neural network has some parameter like learning rate parameter which is initialized manually. We proposed quantum inspired deep neural network using stacked auto-encoder to solve the problem of classi cation of complex dataset. The learning algorithm of stacked auto-encoder has been optimized using evolutionary quantum computing concept. The proposed algorithms are tested on benchmark datasets along with one real life dataset that is o ine signature dataset which is prepared manually. The proposed algorithms are compared with other state-of-the-art approaches and it is found that, proposed algorithms perform well in comparison to other state-ofthe- art approaches. The proposed algorithms perform better due to optimizing their learning parameter using the evolutionary quantum computing concept. The quantum computing concept is characterized by population dynamics, individual representation, evaluation function. It provides a large search space to nd the optimal value of a parameter using an observation process thus, exploration is achieved. On the other hand, the quantum rotational gate provides exploitation to evolve the optimal value of neural network parameters.