Neural networks are a foundational technology that has driven recent artificial intelligence applications. Deep learning represents a considerable breakthrough in the fifty-year history of neural networks, with convolutional neural networks (CNNs) being a prime example. CNNs are built on multilayer neural network structures and employ error backpropagation method for learning. In contrast, other neural network models, such as radial basis function (RBF) networks and extreme learning machines, which do not rely on error backpropagation, have also been developed. These alternative models perform effectively on small-scale regression tasks. The key advantage of these models is their ability to be trained with minimal computational time, thereby addressing the drawback of the error backpropagation method, which requires substantial computational time. This study examines the differences in performance between RBF networks and general multilayer neural networks that employ error backpropagation. For instance, we compare the estimation accuracy and training time of both methods when applied to gene regulatory network inference. Additionally, we present a technique to enhance estimation accuracy for this problem and explore alternative approaches to improving performance beyond deep learning methods.