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, 

        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  "Google Search: Singular Learning Theory"  and  "Bing Search: Singular Learning Theory"   New research field is now being developed. Thank you very much !