arxivmath.AGcs.NE2026-07-19
Expressivity of Shallow Neural Networks Over Finite Fields
Maksym Zubkov, Carol Wu, Shiwei Yang, Param Mody, Yifei Chen
We study the expressivity of shallow polynomial neural networks (PNNs) with monomial activation functions over finite fields. For a given architecture, we define a neuromanifold as the image of the map from all possible network weights into the product of polynomial rings. We qua…