Newton’s Method Backpropagation for Complex-Valued Holomorphic Neural Networks: Algebraic and Analytic Properties

Complex-valued neural networks (CVNNs) have been widely applied in various fields, primarily signal processing and image recognition. Few studies focused on the generalisation of CVNNs, although it is vital to ensure performance CVNNs unseen data. This study first prove a bound for complex-valued networks. The bounds increase as spectral complexity increases, with dominant factor being product ...

It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid...

With the growth in size and complexity of integrated circuits, test generation for them is becoming increasingly difficult, so it is important to find new and effective digital integrated circuit test generation algorithm. In order to improve the quality of combinational test generation, a combinational circuits test generation algorithm based three-valued neural networks [1] is proposed in thi...

Knowledge-Based Artificial Neural Networks (KBANNs) offer a means for combining symbolic and connectionist approaches into a hybrid methodology capable of dealing with small datasets and requires shorter training time when compared to conventional artificial neural networks (ANNs). These approaches were developed mainly for binary-valued domain problems and when applied to real-valued data, man...

Monte Carlo simulations away from half filling suffer a sign problem that can be reduced by deforming the contour of integration. Such transformation, which induces Jacobian determinant in Boltzmann weight, implemented using neural networks. This additional cost for generic network scales cubically with volume, preventing large-scale simulations. We implement an architecture, based on complex-v...