Shun-ichi Amari receives the 2025 Kyoto Prize

A mathematical engineer

Shun-ichi Amari is a mathematical engineer at Teikyo University and an Honorary Science Advisor at RIKEN. In 2025 he was named a laureate of the Kyoto Prize in the field of Advanced Technology, Information Science.^[1] The achievement digest for his award is titled "Pioneering Contributions to Opening Up Theoretical Foundations of Artificial Intelligence and Establishment of Information Geometry."^[1]

What the citation recognises

The citation credits Amari with pioneering research in artificial neural networks, machine learning and information geometry, achievements that have contributed to the evolution of artificial intelligence.^[1] The three areas named may look separate, but they circle one question: how a system with a limited number of parameters represents what it has learned from data, and how it can tell whether it has learned it well.

Artificial neural networks are computing systems built from many simple units whose connections are adjusted; machine learning is the broader project of making programs improve with data rather than by explicit instruction; information geometry supplies a way of measuring how a model changes as it learns. Much of the visible progress in artificial intelligence arrives as products and benchmarks, while the theory that explains why a method works tends to arrive later and more quietly. The prize singles out work of the second kind.

Information geometry

He established information geometry, a field that studies statistical models using the techniques of differential geometry.^[1] A statistical model can be pictured as a family of probability distributions labelled by parameters, so that each setting of the parameters gives one distribution. Collect all the possible settings and you have a space; differential geometry then supplies the vocabulary — distance, curvature, shortest paths — for asking how far apart two models are and how a model moves as evidence accumulates.

A small example makes the idea concrete. Take a coin whose probability of landing heads is unknown. That probability is a single parameter, and all its possible values form a one-dimensional space. Comparing 0.5 with 0.6 by simple subtraction is not very informative; the more natural measure is how many tosses it would take to tell the two coins apart. Turning that intuition into geometry is what information geometry does.

Randomly connected networks and the brain

His statistical mechanical analysis of randomly connected networks created a theoretical model of information processing in the brain that influenced the development of Hopfield networks and recurrent neural networks.^[1] Statistical mechanics is the physicist's tool for systems made of very many interacting parts: instead of tracking every part, it describes the whole through averages. A network of neurons wired at random is exactly such a system. Hopfield networks are recurrent networks whose dynamics settle into stored states, and recurrent neural networks carry a state from one step to the next, which is how sequences are handled. Both are familiar structures in machine learning today.

The 2025 award

The 2025 laureates were announced on 20 June 2025. The presentation ceremony was held on 10 November 2025 at the Kyoto International Conference Center, and each laureate received 100 million yen in prize money.^[2]

Why it matters

Prizes that honour the opening up of theoretical foundations recognise research whose effect is not a single device but a change in how a field frames its questions. Two strands of Amari's work belong to that category: the theory of learning systems, which concerns why a network learns and what it can learn, and the geometry of statistical models, which gives a language in which questions such as how much information a model carries, or how close two models are, can be written down precisely. Work of this kind does not become obsolete with the next generation of hardware; it supplies a shared language for the people who build the next one.