I am researching on a mathematical analysis of neural networks, which are widely applied as a type of artificial intelligence. A neural network is a model containing multi-dimensional parameters, and its purpose is to determine the parameters so that any input will produce the expected output. For example, given any image of a dog taken in the world, you want to determine the parameters so that the neural network can identify it as a "dog". Such a search for "good" parameters is a multidimensional parameter optimization problem, which is discrete and difficult to handle. In recent years, by using the mean field theory, which regards a multibody system as a single system, some researches have been conducted to rewrite the problem into a continuous and tractable problem called "optimization problem of parameter distribution". I am trying to find a decision rule for parameters that leads to the optimal parameter distribution by dealing with both discrete and continuous problems.

I have been interested in the mathematics behind the technologies we see in our daily lives. I loved to consider how integer theory is used in the background of cryptography, or how Fourier transform is used in the background of CT technology, and so on. When I became a graduate student, I learned that neural networks, a type of artificial intelligence, have a simple structure with only a few nonlinear parts. I remember being shocked by the gap between the simplicity of the structure and the wide range of applications. This led me to want to understand neural networks mathematically as functions, and I am still studying them.

I hope that you will continue to pursue what you like, what you want to do, and what you think is fun. There are few people in the Department of Mathematics at Tohoku University who specialize in the mathematics of neural networks. Therefore, when I have a question that I cannot solve in my mind, no one else can solve it. This period is very painful and I sometimes feel pessimistic. Nevertheless, I am able to continue this research because I have chosen this research project and I am enjoying it deep down in my heart. The feeling of "I love it" is the most important driving force for me. I hope that those of you who are reading this will be able to spend your future days being true to what you "love".