Exact ReLU realization of binary affine refinement iterates via reflection folding and cone switching
We study vector-valued binary affine refinement operators with finitely supported matrix masks and compactly supported continuous piecewise linear input and forcing data. We prove that every finite refinement iterate admits an exact ReLU realization of fixed width and depth linear in the number of iterations. No separation of the forcing profile from the binary cell seams is required. The main mechanism is universal reflection doubling. Pairing each residual profile with its reflection replaces the two binary transition matrices by one fixed block matrix together with a fixed swap involution. The cell-seam identity makes the two branch candidates agree at the tent fold, while their swap-o...
| Authors | Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur |
|---|---|
| Primary category | math.OC |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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