arXiv:2609. 28500v1 Announce Type: cross Abstract: We study exact representability by bias-free shallow polynomial neural networks using algebraic geometry.
By Sepehr Akbari, Shahrzad Jamshidi
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
By Vahid Shahverdi, Giovanni Luca Marchetti, Kathl\'en Kohn
The paper proposes a conjecture that composing a fixed number of distinct nonconstant polynomials with a generic high‑degree polynomial produces linearly independent polynomials, extending Newman–Slater’s theorem. The authors prove the conjecture for two polynomials and for any number when the degrees are bounded, and they show how these results explain the parameter symmetries of deep fully connected neural networks with generic polynomial activations. In particular, for architectures with layer‑specific activations of increasing degree, the conjecture’s proven cases fully characterize the parameter sets that yield the same end‑to‑end network function, and it also resolves the identifiability of shallow polynomial networks.
By Kathl\'en Kohn, Giovanni Luca Marchetti, Alex Massarenti, Massimiliano Mella
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
By Pranavkrishnan Ramakrishnan
arXiv:2511. 19703v2 Announce Type: replace-cross Abstract: We study the dimension and identifiability of neurovarieties associated to polynomial neural networks.
By A. Massarenti, M. Mella
arXiv:2606. 07728v1 Announce Type: new Abstract: It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space.
By Blake B. Gaines, Jinbo Bi