30 lines
1.5 KiB
Markdown
30 lines
1.5 KiB
Markdown
---
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title: "On the fibers and semi-algebraicity of ReLU neuromanifolds"
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source: "arXiv:2606.02826v1"
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authors: "Axel Flinth, Stefano Mereta, Michele Pernice"
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affiliation: "KTH Royal Institute of Technology / WASP"
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year: 2026
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category: "math.AG"
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published: "2026-06-01"
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---
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# On the fibers and semi-algebraicity of ReLU neuromanifolds
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**Authors**: Axel Flinth, Stefano Mereta, Michele Pernice
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**arXiv**: 2606.02826v1 [math.AG]
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**Published**: 2026-06-01
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## Abstract
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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.
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## Key Concepts
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- [[neuromanifold|Neuromanifold]] — function space parametrized by network weights
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- [[neuroalgebraic-geometry|Neuroalgebraic Geometry]] — algebro-geometric study of neural networks
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- [[semi-algebraic-set|Semi-algebraic Set]] — sets defined by polynomial equalities/inequalities
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- [[honest-open-subset|Honest Open Subset]] — region free of hidden symmetries
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- [[hidden-symmetries-neural|Hidden Symmetries]] — symmetries beyond scaling and permutation
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- [[parametrization-map|Parametrization Map]] — weight-to-function mapping
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- [[scaling-permutation-symmetry|Scaling & Permutation Symmetries]] — trivial NN symmetries
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- [[fiber-of-parametrization|Fiber of Parametrization]] — preimage of a function
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