RIKEN Center for Advanced Intelligence Project Mathematical Science Team

Team Leader: Kenichi Bannai (D.Math.Sci)

Japanese Page

Research Summary

Mathematical Science Team is a team consisting of pure mathematician and theoretical physisists with aim of attacking mathematical problem arising in artificial intelligence and machine learning.

Main Research Fields

Mathematics

Research Subjects

Machine Learning

Selected Publications

1. I. Ishikawa, K. Fujii, M. Ikeda, Y. Hashimoto, Y. Kawahara.:
"Metric on nonlinear dynamical systems with Perron-Frobenius operators"
The 32nd Conference on Neural Information Processing Systems (NeurIPS2018), Montreal, Canada.
2. M. Ohnishi, M. Yukawa, M. Johansson, and M. Sugiyama.:
"Continuous-time Value Function Approximation in Reproducing Kernel Hilbert Spaces"
he 32nd Conference on Neural Information Processing Systems (NeurIPS2018), Montreal, Canada.
3.K. Kobayashi, N. Hamada, A. Sannai, A. Tanaka, K. Bannai, and M. Sugiyama.:
"Bezier Simplex Fitting: Describing Pareto Fronts of Simplicial Problems with Small Samples in Multi-objective Optimization," AAAI-19, (2019).
4.K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya.:
"Deep learning and the AdS/CFT correspondence"
Phys. Rev. D98 no. 4, (2018) 046019.
5.Y. Takai.:
"Indivisibility of relative class numbers of totally imaginary quadratic extensions and vanishing of these relative Iwasawa invariants"
Journal of Number Theory 186, (2018), 162-179.
6.K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya.:
"Deep Learning and Holographic QCD"
Phys. Rev. D98 no.10, (2018) 106014.
7. T. Kuwahara, T. Ishii, T. Mori, and N. Hatano.:
"Heating in integrable time-periodic systems"
Phys. Rev. Letters Vol 120, 220602 (2018).
8. M. Ikeda and M. Sobajima.:
"Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data"
Math. Ann., 372, (2018), 1017-1040.
9. M. Ikeda and T. Inui.:
"The sharp estimate of the lifespan for the semilinear wave equation with time-dependent damping"
Diff. Int. Equs., 32, (2019), 1-36.
10.K. Bannai, K. Hagihara, S. Kobayashi, K. Yamada, S. Yamamoto and S. Yasuda.:
"Category of mixed plectic Hodge structures"
arXiv:1705.05522 [math.AG], to appear from the Asian Journal of Mathematics.