

























Abstract:We provide a counterexample to the minimal unimodal conjecture for polynomial neural networks (PNNs) with power activation functions. Fixing the input and output widths, the conjecture states that any minimal filling architecture has unimodal widths for the hidden layers. We found a counterexample via a frontier search and certified it using recursive dimension bounds and symbolic computation. Notably, several subarchitectures of this example exhibit large defect, in contrast with the predominantly small-defect behavior observed in prior examples.
| Subjects: | Machine Learning (cs.LG); Algebraic Geometry (math.AG) |
| Cite as: | arXiv:2605.09609 [cs.LG] |
| (or arXiv:2605.09609v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.09609 arXiv-issued DOI via DataCite (pending registration) |
From: Jose Rodriguez [view email]
[v1]
Sun, 10 May 2026 15:46:00 UTC (28 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。