AI RESEARCH
Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements
arXiv CS.LG
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ArXi:2605.01655v1 Announce Type: cross We study homogeneous refinement operators \((V\gamma)(t)=\sum_{j\in\mathbb Z}A_j\gamma(Mt-j)\), acting on compactly ed continuous piecewise linear curves \(\gamma:\mathbb R\to\mathbb R^p\), where \(M\ge2\) and only finitely many matrices \(A_j\in\mathbb R^{p\times p}\) are nonzero. We prove that the iterates \(V^n\gamma\) admit exact ReLU realizations of fixed width and depth \(O(n)\). The main new ingredient is an exact loop controller for the residual dynamics.