ABSTRACT
The brain is an enormously complex system having a rich structure and flexible information processing ability. It is a highly parallel, distributed and modifiable system different from the modern computer architecture. It is important to understand the system-theoretic aspects of the brain, such as how information is represented in the brain and what algorithms the brain uses to solve specific tasks of mental activities. The brain should have realized principles of information processing other than those of modern computers through a long history of evolution. Such principles should be analyzed mathematically by using abstract and idealized models of neural networks. The present section remarks on historical efforts and recent trends in mathematical approaches to (i) multilayer networks, (ii) recurrent networks and (iii) information geometry.
