Shun-ichi Amari

Overview

Shun-ichi Amari, born in 1936, is a mathematical engineer. He serves as Specially Appointed Professor at Teikyo University and as Honorary Science Advisor at RIKEN^[1]. His work sits at the meeting point of statistics, geometry and the theory of computation, and it is cited as groundwork for modern artificial intelligence.

The 2025 Kyoto Prize

Amari is a 2025 laureate of the Kyoto Prize in the Advanced Technology category, in the field of Information Science^[1]. The 2025 laureates were announced on 20 June 2025. Each laureate receives prize money of 100 million yen from the Inamori Foundation, which was established in 1984 by Kyocera founder Kazuo Inamori^[2]. The Kyoto Prize digest credits him with pioneering contributions to opening up the theoretical foundations of artificial intelligence and with the establishment of information geometry^[1].

Information geometry

Amari established the field of information geometry, which studies statistical models using the techniques of differential geometry^[1]. The idea is to treat a family of probability distributions as a kind of curved space: each setting of a model's parameters is a point, and changing the parameters moves you across that space. Because the space is generally not flat, distances and straight lines behave differently from ordinary Euclidean geometry, and tools such as curvature and geodesics can be used to describe how models relate to one another. This gives a common language for questions about estimation, approximation and uncertainty that had previously been handled separately in statistics.

Learning theory and networks of neurons

His research on neural network learning theory proposed the theory of adaptive pattern classifiers, establishing a foundational framework for machine learning^[1]. The question there is how a system that classifies patterns can adjust itself from examples rather than being programmed by hand. Amari also carried out a statistical mechanical analysis of randomly connected networks, which created a theoretical model of information processing in the brain and influenced the development of Hopfield networks and recurrent neural networks^[1]. Treating a network of many simple units with random connections as a physical system allowed its collective behaviour to be described statistically, an approach that later became central to the theory of associative memory and sequence-processing networks.

The natural gradient method

In the 1990s Amari proposed the natural gradient method for machine learning optimization^[1]. Ordinary gradient descent takes a step in the direction that reduces error fastest in the raw coordinates of the parameters, but those coordinates are arbitrary: rescaling one parameter changes the direction of steepest descent. The natural gradient corrects for this by measuring the step in terms of the geometry of the space of models rather than the raw parameters, so that the update does not depend on how the model happens to be parameterized. The method has been applied in neural network learning, blind source separation and Bayesian inference^[1].

Place in the field

Taken together, these strands — a geometry of statistical models, a theory of how classifiers adapt, a statistical physics of network computation and a geometry-aware optimization rule — form a body of theory that machine learning draws on when it asks why learning methods work and how they can be made to work better. Amari's current positions at Teikyo University and RIKEN, and the 2025 Kyoto Prize in Information Science, reflect that standing^[1].