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LM Based Training Algorithm for Quantum Neural Networks

Zhang Yi-pen

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Aiming at the question that the result trained by quantum neural networks is easy to fall into the local least value,the Levenberg-Marquardt algorithm was introduced into the original training algorithm to increase the training speed and improve the performance of the network.In addition,the conflict between different objective functions used for the training synaptic weights and quantum intervals can cause mean square error fluctuates.In order to solve this problem,the iteration order of the original training algorithm was adjusted.The experimental results show that,compared with the original training algorithm,the algorithm using LM can significantly reduce the number of iterations,significantly decrease the mean square error when the network convergences,and improve the classification results of quantum neural network.

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Aiming at the question that the result trained by quantum neural networks is easy to fall into the local least value,the Levenberg-Marquardt algorithm was introduced into the original training algorithm to increase the training speed and improve the performance of the network.In addition,the conflict between different objective functions used for the training synaptic weights and quantum intervals can cause mean square error fluctuates.In order to solve this problem,the iteration order of the original training algorithm was adjusted.The experimental results show that,compared with the original training algorithm,the algorithm using LM can significantly reduce the number of iterations,significantly decrease the mean square error when the network convergences,and improve the classification results of quantum neural network.
Inspired by the principle of superposing states in quantum mechanics,a new kind of feedforward neural network with single hidden layer was designed and named as Quantum Neural Networks.It has mainly been used for data classification.Multilevel activation functions is adopted in Quantum Neural Networks and a different objective function is used for the learning of quantum intervals of the multilevel hidden units;minimizing the class-conditional variances at the outputs of the hidden units.Quantum Neural Networks is endowed with a special ability of identifying uncertainty in data classification by its unique design.However,as different objective functions are used for the learning of synaptic weights and quantum intervals,conflict is observed in the iterative training process which will cause more iteration times for training and degrades the training results.Using the theory of Constrained Optimization,a new training algorithm is proposed in this paper by introducing penalty function into the steepest descent method.In the new training algorithm, the conflict is removed.Experimental results indicate that the new algorithm can increase the training speed and improve the performance of the trained network remarkably.
This article proposes a model of a quantum neural network based on a multilevel activation function, which has high performance. This performance is achieved by combining such unique components as: the quantum weight vector, quantum activity values and the dot product operator. In addition, algorithms for learning weight parameters and quantum intervals are presented, in particular, the Levenberg-Marquardt algorithm is improved to improve the quality of the error back propagation method in the process of learning weight parameters, which will also reduce the likelihood of quantum errors.
In the structure of original Quantum Neural Network (QNN), only multi-sigmoid transfer function is adopted. Besides that, due to the conflict of the two objective functions in original training algorithm, the training process converges slowly and presents constant variation. In this paper, the QNN with multi-tan-sigmoid transfer function and a novel training algorithm which combines the two objective functions are proposed. Experimental results demonstrate the effectiveness of the structure improvement and the new training algorithm. Streszczenie. W oryginalnym algorytmie kwantowej sieci neuronowej QNN tylko multisigmoidalna funkcja przejścia jest wykorzystywana. W pracy zaprezentowano siec z multi-tan-sigmoidalną funkcją przejścia z nowym algorytmem uczenia. (Nowa struktura i algorytm uczenia w kwantowej sieci neuronowej)
This paper reports the performance of a novel training algorithm for quantum neural networks (QNN) using a variation of the quantum search algorithm. The proposed algorithm trains a QNN exploring all possible weights with a sublinear cost. The training cost is theoretically O(√(N/t)), as a function of the quantity N of possible weights and t is the number of possible solutions. Initial experimental results demonstrate that the algorithm always converges to existing solutions, in addition to having the mean and maximum values, almost in total, lower than the expected maximum amount, as theoretically expected. The training algorithm is applied to classification problems.
The current status of Quantum Neural Network (QNN) research is analyzed, it deeply studies the model Quantum Gate Circuit Neural Network (QGCNN) and QGCNN Learning Algorithm (QGCA). Replacing the mean square error function by using the Widrow function and the Rumelhart function, it creates two quantum neural network learning algorithms based on performance function, including Learning Algorithm of QGCNN based on the Widrow functions (WQGCA) and Learning Algorithm of QGCNN based on the Rumelhart functions (RQGCA). New algorithms overcome the inherent defects of the training result is not ideal and unrealistic, which is because the use of mean square error function training network will appear excessive punishment phenomenon. Three algorithms are trained by three data sets. Simulation Experiments on three kinds of algorithms was carried out by using these data sets in the case of the best learning rate. Research prove WQGCA and RQGCA have better pattern classification ability relative to QGCA and RQGCA has a higher classification accuracy than WQGCA.
In this paper a novel quantum based binary neural network learning algorithm is proposed. It forms three layer network structure. The proposed method make use of quantum concept for updating and finalizing weights of the neurons and it works for two class problem. The use of quantum concept form an optimized network structure. Also performance in terms of number of neurons and classification accuracy is improved. Same is compared with a quantum-based algorithm for optimizing artificial neural networks algorithm (QANN). It is found that there is improvement in the form of number of neurons at hidden layer, number of iterations, training accuracy and generalization accuracy.