Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.09525 |
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Sommario:
- The complexity of continuous piecewise affine (CPA) functions can be measured by the number of pieces $p$ or the number of distinct affine functions $n$. For CPA functions on $\mathbb{R}^d$, this paper shows an upper bound of $p=O(n^{d+1})$ and constructs a family of functions achieving a lower bound of $p=Ω(n^{d+1-\frac{c}{\sqrt{\log_2(n)}}})$.