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International Joint Conference on Neural Networks (IJCNN)

Quantum Morphogenetic System in image recognition

Germano Resconi, Chu Kiong Loo, Nuo Wi Tay

Published Jun 1, 2009• 2 citations
Publisher

Abstract

Hopfield network requires that state vectors of images to be orthogonal to eliminate cross-talk. In practical sense, it cannot be achieved. A solution is to orthogonalize the state vectors with each other as a pre-processing. The QMS (Quantum Morphogenetic System) is a mathematical model devised to give a different more elegant and intuitive perspective of the pre-processing by assuming a non-Euclidean geometry. Input image is projected to the feature vector in terms of its contra-variant components which are interdependent. Image reconstruction is achieved by parallelogram summation of the vector of those components. Besides, an extension to Holonomic brain model and tensor network theory is discussed.

DOI
10.1109/ijcnn.2009.5178846

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Hopfield network requires that state vectors of images to be orthogonal to eliminate cross-talk. In practical sense, it cannot be achieved. A solution is to orthogonalize the state vectors with each other as a pre-processing. The QMS (Quantum Morphogenetic System) is a mathematical model devised to give a different more elegant and intuitive perspective of the pre-processing by assuming a non-Euclidean geometry. Input image is projected to the feature vector in terms of its contra-variant components which are interdependent. Image reconstruction is achieved by parallelogram summation of the vector of those components. Besides, an extension to Holonomic brain model and tensor network theory is discussed.
The storage capacity of the conventional Hopfield network is the 0.14 times of the number of neurons(P=0.14N). Because of the huge difficulty in recognizing a large number of images or patterns, researchers are looking for new methods at all times. Quantum neural network (QNN) is a young and outlying science built upon the combination of classical neural network and quantum computing. A Quantum Hopfield neural network (QHNN) whose elements of the storage matrix are distributed in a probability way on the base of quantum linear superposition is presented for speeding up the images recognition and increasing the number of the images recognition. Contrasting to the conventional Hopfield neural network, the storage capacity of the QHNN is increased by a factor of 2N, where N is the number of neurons. Besides, the case analysis and simulation tests have been carried out for the recognition of images in this paper. The result indicates that QHNN can recognize the images or patterns effectively and its working process accords with quantum evolvement process.
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of qubit spaces). For example, for algorithm of factorization of numbers by quantum computer n can be about a few hundreds for some realistic applications for cryptography. The applications described further are used some other properties of quantum systems and they do not demand such huge number of states. The term "images recognition" is used here for some broad class of problems. For example, we have a set of some objects V_i and function of "likelihood": F(V,W) < F(V,V) = 1 If we have some "noisy" or "distorted" image W, we can say that recognition of W is V_i, if F(W,V_i) is near 1 for some V_i.
Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understanding of the working mechanisms and improve the performance of both models.
Abstract Quantum computing is a new mode that follows the laws of quantum mechanics. It performs computational tasks based on the control of quantum units. From the view of computable problems, quantum computers can only solve the problems that traditional computers can solve, but considering the efficiency of computation, due to the existence of quantum superposition, some known quantum algorithms are exponentially faster than traditional general-purpose computers. In this article, we combine quantum computing with a classical neural network to design a quantum Hopfield network. Each neuron is initialized to a specified state and evolved into a steady state. The output result is one of patterns in a training set. We also present an application of this protocol in image recognition. The simulation results show that this network works in the quantum environment and the output images are correct, therefore the feasibility of this protocol is verified.
The classical neural network has provided remarkable results to diagnose neurological disorders against neuroimaging data. However, in terms of efficient and accurate classification, some standpoints need to be improved by utilizing high-speed computing tools. By integrating quantum computing phenomena with deep neural network approaches, this study proposes an AlexNet–quantum transfer learning method to diagnose neurodegenerative diseases using magnetic resonance imaging (MRI) dataset. The hybrid model is constructed by extracting an informative feature vector from high-dimensional data using a classical pre-trained AlexNet model and further feeding this network to a quantum variational circuit (QVC). Quantum circuit leverages quantum computing phenomena, quantum bits, and different quantum gates such as Hadamard and CNOT gate for transformation. The classical pre-trained model extracts the 4096 features from the MRI dataset by using AlexNet architecture and gives this vector as input to the quantum circuit. QVC generates a 4-dimensional vector and to transform this vector into a 2-dimensional vector, a fully connected layer is connected at the end to perform the binary classification task for a brain disorder. Furthermore, the classical–quantum model employs the quantum depth of six layers on pennyLane quantum simulators, presenting the classification accuracy of 97% for Parkinson’s disease (PD) and 96% for Alzheimer’s disease (AD) for 25 epochs. Besides this, pre-trained classical neural models are implemented for the classification of disorder and then, we compare the performance of the classical transfer learning model and hybrid classical–quantum transfer learning model. This comparison shows that the AlexNet–quantum learning model achieves beneficial results for classifying PD and AD. So, this work leverages the high-speed computational power using deep network learning and quantum circuit learning to offer insight into the practical application of quantum computers that speed up the performance of the model on real-world data in the healthcare domain.