Shun-ichi Amari
RIKEN Brain Science Institute

Abstract
The brain encodes information in the form of excitation patterns of neurons, and processes it stochastically. It realizes reliable computation by using stochastically fluctuating neurons. Population coding is a typical form of information representation in the brain, where neural systems perform Bayesian inference. The present talk overviews the principles of population coding, amount of information encoded in it, and the Bayesian method of inference in the brain. Information geometry is a mathematical tool to elucidate a family of probability distributions. We analyze the structure of higher-order correlations of neural firing, and show how it is related to synchronous firing. Information geometry is not only useful for analyzing population coding, but also plays a fundamental role in understanding artificial neural networks such as multilayer perceptrons. Mathematical neuroscience is becoming more important, and this serves as an introduction to it.

Speaker
Shun-ichi Amari was born in Tokyo, Japan, on January 3, 1936. He graduated from the Graduate School of the University of Tokyo in 1963 majoring in mathematical engineering and received the Dr. Eng. Degree.
He worked as an Associate Professor at Kyushu University and the University of Tokyo, and then a Full professor at the University of Tokyo, and is now Professor-Emeritus. He serves now as Director of RIKEN Brain Science Institute. He has been engaged in research in wide areas of mathematical engineering, such as topological network theory, differential geometry of continuum mechanics, pattern recognition, and information sciences. In particular, he has devoted himself to mathematical foundations of neural network theory, including statistical neurodynamics, dynamical theory of neural fields, associative memory, self-organization, and general learning theory. Another main subject of his research is information geometry initiated by himself, which applies modern differential geometry to statistical inference, information theory, control theory, stochastic reasoning, and neural networks, providing a new powerful method of information sciences and probability theory.
Dr. Amari is President of Institute of Electronics, Information and Communication Engineers, Japan, and past President of International Neural Networks Society. He received the Emanuel A. Piore Award and the Neural Networks Pioneer Award from the IEEE, the Japan Academy Award, the C&C award, among many others.