Research
The Alexander-Hirschowitz theorem for neurovarieties
arXiv:2511.19703v2 Announce Type: replace-cross Abstract: We study the dimension and identifiability of neurovarieties associated to polynomial neural networks. We give an independent geometric proof
arXiv:2511.19703v2 Announce Type: replace-cross Abstract: We study the dimension and identifiability of neurovarieties associated to polynomial neural networks. We give an independent geometric proof that the linear bounds d_igeq 2n_i-1 on the activation degrees imply non defectiveness for any number of outputs, a dimension statement previously obtained from finite identifiability. The proof is based on a direct analysis of the differential of the parameterization. We also investigate secant and Grassmann-secant obstructions outside this range and prove global identifiability for multi-output architectures under the same degree bounds.
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Source: arXiv cs.AI | 2026-09-02