Adaptive complex-valued stepsize based fast learning of complex-valued neural networks

Complex-valued soft-log threshold reweighting for sparsity of complex-valued convolutional neural networks

Complex-valued convolutional neural networks (CVCNNs) have been demonstrated effectiveness in classifying complex signals and synthetic aperture radar (SAR) images. However, due to the introduction of complex-valued parameters, CVCNNs tend to become redundant with heavy floating-point operations. Model sparsity is emerged as an efficient method of removing the redundancy without much loss of performance. Currently, there are few studies on the sparsity problem of CVCNNs. Therefore, a complex-valued soft-log threshold reweighting (CV-SLTR) algorithm is proposed for the design of sparse CVCNN to reduce the number of weight parameters and simplify the structure of CVCNN. On one hand, considering the difference between complex and real numbers, we redefine and derive the complex-valued log-sum threshold method. On the other hand, by considering the distinctive characteristics of complex-valued convolutional (CConv) layers and complex-valued fully connected (CFC) layers of CVCNNs, the complex-valued soft and log-sum threshold methods are respectively developed to prune the weights of different layers during the forward propagation, and the sparsity thresholds are optimized during the backward propagation by inducing a sparsity budget. Furthermore, different optimizers can be integrated with CV-SLTR. When stochastic gradient descent (SGD) is used, the convergence of CV-SLTR is proved if Lipschitzian continuity is satisfied. Experiments on the RadioML 2016.10A and S1SLC-CVDL datasets show that the proposed algorithm is efficient for the sparsity of CVCNNs. It is worth noting that the proposed algorithm has fast sparsity speed while maintaining high classification accuracy. These demonstrate the feasibility and potential of the CV-SLTR algorithm.

Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall-Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov-Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.

Adaptive CL-BFGS Algorithms for Complex-Valued Neural Networks

Complex-valued limited-memory BFGS (CL-BFGS) algorithm is efficient for the training of complex-valued neural networks (CVNNs). As an important parameter, the memory size represents the number of saved vector pairs and would essentially affect the performance of the algorithm. However, the determination of a suitable memory size for the CL-BFGS algorithm remains challenging. To deal with this issue, an adaptive method is proposed in which the memory size is allowed to vary during the iteration process. Basically, at each iteration, with the help of multistep quasi-Newton method, an appropriate memory size is chosen from a variable set {1,2, ... , M} by approximating complex Hessian matrix as close as possible. To reduce the computational complexity and ensure desired performance, the upper bound M is adjustable according to the moving average of memory sizes found in previous iterations. The proposed adaptive CL-BFGS (ACL-BFGS) algorithm can be efficiently applied for the training of CVNNs. Moreover, it is suggested to take multiple memory sizes to construct the search direction, which further improves the performance of the ACL-BFGS algorithm. Experimental results on some benchmark problems including the pattern classification, complex function approximation, and nonlinear channel equalization problems are given to illustrate the advantages of the developed algorithms over some previous ones.

Fully Complex-Valued Dendritic Neuron Model

A single dendritic neuron model (DNM) that owns the nonlinear information processing ability of dendrites has been widely used for classification and prediction. Complex-valued neural networks that consist of a number of multiple/deep-layer McCulloch-Pitts neurons have achieved great successes so far since neural computing was utilized for signal processing. Yet no complex value representations appear in single neuron architectures. In this article, we first extend DNM from a real-value domain to a complex-valued one. Performance of complex-valued DNM (CDNM) is evaluated through a complex XOR problem, a non-minimum phase equalization problem, and a real-world wind prediction task. Also, a comparative analysis on a set of elementary transcendental functions as an activation function is implemented and preparatory experiments are carried out for determining hyperparameters. The experimental results indicate that the proposed CDNM significantly outperforms real-valued DNM, complex-valued multi-layer perceptron, and other complex-valued neuron models.

A training algorithm with selectable search direction for complex-valued feedforward neural networks

This paper focuses on presenting an efficient training algorithm for complex-valued feedforward neural networks by utilizing a tree structure. The basic idea of the proposed algorithm is that, by introducing a set of direction factors, distinctive search directions are available to be selected at each iteration such that the objective function is reduced as much as possible. Compared with some well-known training algorithms, one of the advantages of our algorithm is that the determination of search direction is of great flexibility and thus more accurate solution is obtained with faster convergence speed. Experimental simulations on pattern recognition, channel equalization and complex function approximation are provided to verify the effectiveness and applications of the proposed algorithm.