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+title: "On the fibers and semi-algebraicity of ReLU neuromanifolds"
+source: "arXiv:2606.02826v1"
+authors: "Axel Flinth, Stefano Mereta, Michele Pernice"
+affiliation: "KTH Royal Institute of Technology / WASP"
+year: 2026
+category: "math.AG"
+published: "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|Neuromanifold]] — function space parametrized by network weights
+- [[neuroalgebraic-geometry|Neuroalgebraic Geometry]] — algebro-geometric study of neural networks
+- [[semi-algebraic-set|Semi-algebraic Set]] — sets defined by polynomial equalities/inequalities
+- [[honest-open-subset|Honest Open Subset]] — region free of hidden symmetries
+- [[hidden-symmetries-neural|Hidden Symmetries]] — symmetries beyond scaling and permutation
+- [[parametrization-map|Parametrization Map]] — weight-to-function mapping
+- [[scaling-permutation-symmetry|Scaling & Permutation Symmetries]] — trivial NN symmetries
+- [[fiber-of-parametrization|Fiber of Parametrization]] — preimage of a function