Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space

Deep learning has achieved notable success in various fields, including image and speech recognition. One of the factors successful performance deep is its high feature extraction ability. In this study, we focus on adaptivity learning; consequently, treat variable exponent Besov space, which a different smoothness depending input location x. other words, difficulty estimation not uniform within domain. We analyze general approximation error space errors learning. note that improvement based remarkable when region upon target function less small dimension large. Moreover, superiority to linear estimators shown with respect convergence rate error.