Shun-ichi Amari (born 1936) is a Japanese mathematical engineer and neuroscientist who provided much of the mathematical foundation for artificial neural networks. As early as 1967 he analyzed the training of multilayer networks using a stochastic-gradient learning rule, well before such methods became mainstream. He spent his career at the University of Tokyo and at RIKEN, where he led the Brain Science Institute.
In the 1980s Amari founded the field he named information geometry, which applies the tools of differential geometry to families of probability distributions and statistical models. Out of this came his 1990s natural-gradient method, an optimization technique that accounts for the geometric structure of a model’s parameter space rather than treating all directions as equivalent, and which can make learning markedly more efficient. These ideas now reach into statistics, signal processing, optimization, and the training of modern deep networks.
In 2025 Amari received the Kyoto Prize in Advanced Technology, whose citation recognized his “pioneering research in the fields of artificial neural networks, machine learning, and information geometry.” His career is a reminder that the theory underpinning today’s neural networks was built up over decades by mathematicians whose names are far less familiar than the systems their work made possible.