PreprintCC BY 4.0arXiv
Minimal Filling Architectures for Polynomial Neural Networks
Abstract
Minimal filling architectures describe the smallest hidden-layer widths for which the neurovariety of a polynomial neural network fills its ambient function space. It was conjectured that every such architecture has unimodal hidden widths. We construct counterexamples to this conjecture using a frontier search and certify the main example through finite-field Jacobian computations and recursive dimension bounds. In the opposite direction, we prove that every minimal filling architecture of depth at most three is unimodal. A nonunimodal minimal filling architecture of depth four shows that the depth bound is sharp.
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BibTeX
@misc{dao2026minimal,
title = {{Minimal Filling Architectures for Polynomial Neural Networks}},
author = {Kevin Dao and Jose Israel Rodriguez},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.09609},
eprint = {2605.09609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal Filling Architectures for Polynomial Neural Networks
AU - Kevin Dao
AU - Jose Israel Rodriguez
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.09609
UR - https://arxiv.org/abs/2605.09609
AB - Minimal filling architectures describe the smallest hidden-layer widths for which the neurovariety of a polynomial neural network fills its ambient function space. It was conjectured that every such architecture has unimodal hidden widths. We construct counterexamples to this conjecture using a frontier search and certify the main example through finite-field Jacobian computations and recursive dimension bounds. In the opposite direction, we prove that every minimal filling architecture of depth at most three is unimodal. A nonunimodal minimal filling architecture of depth four shows that the depth bound is sharp.
ER -