The Alexander-Hirschowitz theorem for neurovarieties
Quick summary
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 $d_i\geq 2n_i-1$ 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-outp
Key takeaways
- 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 $d_i\geq 2n_i-1$ 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.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
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