Double framed moduli spaces of quiver representations
| Autor: | Marco Armenta, Thomas Brüstle, Souheila Hassoun, Markus Reineke |
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| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Numerical Analysis Algebra and Number Theory Computer Science - Neural and Evolutionary Computing Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 16G20 14D22 53D30 68T01 68T07 FOS: Mathematics Discrete Mathematics and Combinatorics Neural and Evolutionary Computing (cs.NE) Geometry and Topology Representation Theory (math.RT) Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics - Representation Theory |
| Zdroj: | Linear Algebra and its Applications. 650:98-131 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2022.05.018 |
| Popis: | Motivated by problems in the neural networks setting, we study moduli spaces of double framed quiver representations and give both a linear algebra description and a representation theoretic description of these moduli spaces. We define a network category whose isomorphism classes of objects correspond to the orbits of quiver representations, in which neural networks map input data. We then prove that the output of a neural network depends only on the corresponding point in the moduli space. Finally, we present a different perspective on mapping neural networks with a specific activation function, called ReLU, to a moduli space using the symplectic reduction approach to quiver moduli. 27 pages |
| Databáze: | OpenAIRE |
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