{"ID":2830815,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.09853","arxiv_id":"2512.09853","title":"New Approximation Results and Optimal Estimation for Fully Connected Deep Neural Networks","abstract":"\\citet{farrell2021deep} establish non-asymptotic high-probability bounds for general deep feedforward neural network (with rectified linear unit activation function) estimators, with \\citet[Theorem 1]{farrell2021deep} achieving a suboptimal convergence rate for fully connected feedforward networks. The authors suggest that improved approximation of fully connected networks could yield sharper versions of \\citet[Theorem 1]{farrell2021deep} without altering the theoretical framework. By deriving approximation bounds specifically for a narrower fully connected deep neural network, this note demonstrates that \\citet[Theorem 1]{farrell2021deep} can be improved to achieve an optimal rate (up to a logarithmic factor). Furthermore, this note briefly shows that deep neural network estimators can mitigate the curse of dimensionality for functions with compositional structure and functions defined on manifolds.","short_abstract":"\\citet{farrell2021deep} establish non-asymptotic high-probability bounds for general deep feedforward neural network (with rectified linear unit activation function) estimators, with \\citet[Theorem 1]{farrell2021deep} achieving a suboptimal convergence rate for fully connected feedforward networks. The authors suggest...","url_abs":"https://arxiv.org/abs/2512.09853","url_pdf":"https://arxiv.org/pdf/2512.09853v1","authors":"[\"Zhaoji Tang\"]","published":"2025-12-10T17:36:00Z","proceeding":"econ.EM","tasks":"[\"econ.EM\",\"stat.ML\"]","methods":"[]","has_code":false}