Work

Minimal Filling Architectures for Polynomial Neural Networks

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.09609

Authors: Dao, Kevin, Rodriguez, Jose Israel

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation

Awards: Applied Algebraic Geometry: Polynomial Neural Networks, Graduate Research Fellowship Program (GRFP)

OpenAlex ID: W7160951764

Cites: 2

Cited by: 1

Related to: 10