Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks
arXiv:2607.01266v1 Announce Type: cross Abstract: 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 accu
This paper presents foundational theoretical work on approximating complex decision boundaries in AI, a critical step towards more robust and efficient neural networks.
Sophisticated readers should care as this research contributes to the mathematical understanding and practical capabilities of AI, particularly in areas requiring precise classification and interpretation of complex data.
The theoretical understanding of how effectively ReLU neural networks can approximate complex classification tasks within o-minimal structures is advanced, potentially leading to more efficient future AI models.
- · AI researchers
- · Machine learning developers
- · High-performance computing sector
Improved theoretical understanding of ReLU neural network capabilities for complex classification tasks.
Potential for development of more robust, efficient, and provably accurate AI systems for decision-making.
Accelerated deployment of AI in critical applications where accuracy and predictability are paramount.
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