Dreaming of Mathematical Neuroscience for Half a Century

AL4 Dreaming of Mathematical Neuroscience for Half a Century ○甘利俊一1 ○Shun-ichi Amari1 理化学研究所 脳科学総合研究センター特別顧問1 " I have been dreaming of mathematical neuroscience for nearly half a century. What is mathematical neuroscience and what is its role in brain science? Information in the brain is widely distributed over networks of neurons and processed by parallel dynamics. It has learning and self-organizing capabilities. I believe that there are fundamental principles based on which outstanding information processing takes place due to parallel distributed dynamics with self-organization. As our brains have implemented such principles through their extremely long history of evolution, it is not easy to understand the principles. The brain has indeed emerged via a long history of evolution, so that its principles are largely different from those of physics or chemistry. Even though the principles of complex phenomena in everyday life are hidden in the world of physics, one may think of extreme situations where the fundamental principles can be directly observed. However, the brain is a living organ that cannot survive in extreme situations. As it is a highly complex system, we wonder whether it really is possible to discover mathematical principles in it. We need to construct ideal models of information processing to elucidate such principles, in which parallel dynamics takes place and information is widely distributed. Mathematical analysis of the models would hopefully make it possible to understand the underlying principles. Although the actual brain is different from simple models, I believe that the same principles would work even in very complex actual brains. As simple forms of principles are insufficient to understand the real brain, we also need to find how the principles are substantialized in the actual brain. Here comes the role of computational neuroscience, which seeks for computational aspects of realistic neural networks, but is different from mathematical neuroscience. My research began nearly fifty years ago when I was striving to discover the principles of the brain mathematically by using typical simple models of neural networks. I will show the following three examples in order to introduce you to the world of mathematical neuroscience and to convince you its importance. 1) Statistical neurodynamics: dynamics of randomly connected neurons 2) Dynamics of neural fields: retention, propagation and development of excitation patterns in a neural field 3) Information geometry of neuronal spikes: orthogonal decomposition of higher-order interactions of spikes"

上部に戻る

前に戻る