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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2512.09853 |
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| _version_ | 1866911311510634496 |
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| author | Tang, Zhaoji |
| author_facet | Tang, Zhaoji |
| contents | \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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Approximation Results and Optimal Estimation for Fully Connected Deep Neural Networks Tang, Zhaoji Econometrics Machine Learning \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. |
| title | New Approximation Results and Optimal Estimation for Fully Connected Deep Neural Networks |
| topic | Econometrics Machine Learning |
| url | https://arxiv.org/abs/2512.09853 |