AIP Math Team Seminar

Speaker:Dr. Koichi Taniguchi (Nagoya University)

Title: On approximation ability for Besov space by deep ReLU network

Abstract: Recently, it has been shown that deep learning outperforms any
linear estimator such as kernel ridge regression, where the
target function has highly spatial inhomogeneity of its
smoothness. To generalize these results, we consider the
approximation and estimation error bounds of deep ReLU networks
where the target function is in a Besov space with variable
smoothness. The Besov space is a function space with three
exponents (i.e., smoothness exponent, integrability exponent
and interpolation exponent), which includes H\"older space
and Sobolev space. This talk is based on the joint work with
Sho Sonoda (RIKEN), Masahiro Ikeda (RIKEN/ Keio Univ.),
Kenta Oono (Tokyo Univ./Preferred Networks), and
Taiji Suzuki (Tokyo Univ./RIKEN).