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Welcome to Sumio Watanabe Homepage.
Welcome to Sumio Watanabe Homepage.
Here I would like to explain mathematics which is connected to statistical learning theory. You will find a fantastic road,
Here I would like to explain mathematics which is connected to statistical learning theory. You will find a fantastic road,
Algebraic Geometry
---> Gelfand Zeta Function
---> Schwartz Distribution
---> Empirical Process
---> Statistical Learning Theory,
which shall take you clear understanding deep learning process and further exploration.
I'm very happy that so many people are interested in and cooperating with singular learning theory. Please enjoy many researchers' new wonderful results by "Bing Search: Singular Learning Theory" and "Google Search: Singular Learning Theory" . For lectures, Youtube: Singular Learning Theory . New research field is now being developed. Thank you very much for your interest !
Dr. Sumio Watanabe is a professor emeritus at Institute of Science Tokyo (Former Tokyo Institute of Technology), a visiting senior researcher of RIKEN, and an IEICE fellow.
New Information :
On October 27th 2025, I will give a lecture at Tohoku University. The title of my talk is 'Introduction to singular learning theory'. This lecture is delivered in Japanese.
Abstract. Deep neural networks used in the realization of artificial intelligence are redundant with respect to the functions they represent, and the rank of the Fisher information matrix is significantly smaller than the dimensionality of the parameter space. Singular learning theory has been developed to mathematically handle the learning and prediction of such models with singular characteristics. This seminar is designed for those encountering singular learning theory for the first time, offering a clear overview of the topic and exploring its potential applications to AI alignment, an area of active research in recent years.
Recent Articles :
(1) Sumio Watanabe, Review and prospect of algebraic research in equivalent framework between statistical mechanics and machine learning theory, Reviews in Mathematical Physics. arxiv.org/abs/arxiv2406.10234v3
(2) S. Watanabe, Mathematical theory of Bayesian statistics for unknown information source. Philosophical Transactions of Royal Society A, doi.org/10.1098/rsta.2022.0151, 2023. https://arxiv.org/abs/2206.05630
(3) S. Watanabe, Recent advances in algebraic geometry and Bayesian statistics. Information Geometry, doi.org/10.1007/s41884-022-00083, 2022. https://arxiv.org/abs/2211.10049
(4) S. Watanabe, Information criteria and cross validation for Bayesian inference in regular and singular cases. Japanese Journal of Statistics and Data Science, vol.4, pp.1-19, 2021.
In the paper (1), algebraic research in learning theory is discussed on the equivalence between machine learning and statistical mechanics. In the paper (2), unknown uncertainty and statistical model in Bayesian statistics is studied. In the paper (3). algebro-geometric study of Bayesian statistics is introduced. In the paper (4), difference between information criteria and cross validation is explained.
Author : Sumio Watanabe
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