1.5 KiB
1.5 KiB
title, source, authors, affiliation, year, category, published
| title | source | authors | affiliation | year | category | published |
|---|---|---|---|---|---|---|
| On the fibers and semi-algebraicity of ReLU neuromanifolds | arXiv:2606.02826v1 | Axel Flinth, Stefano Mereta, Michele Pernice | KTH Royal Institute of Technology / WASP | 2026 | math.AG | 2026-06-01 |
On the fibers and semi-algebraicity of ReLU neuromanifolds
Authors: Axel Flinth, Stefano Mereta, Michele Pernice arXiv: 2606.02826v1 [math.AG] Published: 2026-06-01
Abstract
We study the semi-algebraicity of the neuromanifold M_d of a feedforward ReLU neural network and its symmetries. We prove that M_d is not a semi-algebraic quotient of the space of weights. We introduce honest open subsets where the network shows no hidden symmetries, conjecture the maximal honest open is always semi-algebraic, and prove it is Zariski open in the shallow case.
Key Concepts
- neuromanifold — function space parametrized by network weights
- neuroalgebraic-geometry — algebro-geometric study of neural networks
- semi-algebraic-set — sets defined by polynomial equalities/inequalities
- honest-open-subset — region free of hidden symmetries
- hidden-symmetries-neural — symmetries beyond scaling and permutation
- parametrization-map — weight-to-function mapping
- scaling-permutation-symmetry — trivial NN symmetries
- fiber-of-parametrization — preimage of a function