Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks
We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field. Motivated by cell decomposition of definable sets, we introduce traceable sets as a classical proxy for definable decision regions and analyze their approximation by ReLU neural networks. Under uniform bounds on the number of connected components and suitable $C^m$ extensions for the boundary functions, we prove that characteristic functions of traceable subsets of $[-1/2,1/2]^n$ can be approximated in $L^p$ to accuracy $\varepsilon>0$ by ReLU neural networks of size $\mathcal{O}(\varepsilon^{-p(n-1)/m})$, with depth independent of $\varepsilon$ and polynomial...
| Authors | Clemens Kinn, Philipp Petersen |
|---|---|
| Primary category | math.LO |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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