Analyzing Artificial Neural Network Design Through Mathematical Principles

Artificial Neural Networks have been around for years and have found an integral place in the development of machine learning and artificial intelligence applications recently. Researchers from diverse backgrounds have contributed to the resurgence of interest in artificial neural networks because of its numerous applications. The behavioral characteristics and computational power of neural networks has made them a captivating alternative for traditional models. In practice, neural network designers face lot of problems in architecture design before being able to develop reasonably good models due to lack of fundamental knowledge. The fear of mathematics drives people from non-mathematical and non-computers background to straight away jump into development of applications based on neural networks without understanding their underlying design. This may result into unexpected results of experiments. Hence, it is important to understand the symbols, their representations, roles and the process by which they are manipulated. This paper covers the basics of neural network design and mathematical modeling of complex cognitive processes. The intention is to make the neural network design and development approach accessible to researchers, practitioners and scientists irrespective of their domains. It can also be a helpful starting point for computer engineers, mathematicians, and interdisciplinary learners. The paper provides a valuable beginning to anyone interested in understanding the fundamentals of neural network design and modelling.