Piecewise linear functions and neural network expressivity via discriminantal arrangements
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911564318113792 |
|---|---|
| author | Das, Pragnya |
| author_facet | Das, Pragnya |
| contents | We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via Mobius inversion, with dimension equal to the number of independent sets. For circuits of size three, functions are determined by values on subsets of size at most two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Piecewise linear functions and neural network expressivity via discriminantal arrangements Das, Pragnya Combinatorics Algebraic Geometry 05B35, 52C35(Primary), 68T07 (Secondary) We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via Mobius inversion, with dimension equal to the number of independent sets. For circuits of size three, functions are determined by values on subsets of size at most two. |
| title | Piecewise linear functions and neural network expressivity via discriminantal arrangements |
| topic | Combinatorics Algebraic Geometry 05B35, 52C35(Primary), 68T07 (Secondary) |
| url | https://arxiv.org/abs/2604.02480 |