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We study neurovarieties for polynomial neural networks and fully characterize when they attain the expected dimension in the single-output case. As consequences, we establish non-defectiveness and global identifiability for multi-output architectures.
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Geometry of Polynomial Neural Networks
Activation degree thresholds and expressiveness of polynomial neural networks
Identifiability of Deep Polynomial Neural Networks
On the Geometry and Optimization of Polynomial Convolutional Networks
Expressivity of Shallow and Deep Neural Networks for Polynomial Approximation
Erzeugunsgrad, VC-Dimension and Neural Networks with rational activation function
@article{massarenti2025alexanderhirschowitz,
title = {The Alexander-Hirschowitz theorem for neurovarieties},
author = {A. Massarenti and M. Mella},
year = {2025},
eprint = {2511.19703},
archivePrefix = {arXiv},
url = {http://arxiv.org/abs/2511.19703v1}
}Shows whether official code is linked for this paper.
[](https://codeofpaper.com/paper/2511.19703)