Neural network realization of binary refinement iterates via a two-chart atlas selector
Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling. Their finite iterates can develop rapidly increasing numbers of linear pieces, making them a natural test case for the expressive power of deep neural networks. Earlier work showed that, for scalar binary refinement with a finitely supported mask, every compactly supported continuous piecewise linear seed has finite refinement iterates that admit exact ReLU realizations of fixed width and depth growing linearly with the number of refinement steps. The present paper gives a new construction of this known theorem. The difficulty is that the refinement cascade is driven by...
| Authors | Tsogtgerel Gantumur |
|---|---|
| Primary category | math.NA |
| Published | 21 July 2026 |
| Last updated at source | 21 July 2026 |
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