Kaehler geometry of quiver varieties and machine learning

Date
DOI
Authors
Lau, Siu-Cheong
Jeffreys, George
Version
First author draft
OA Version
Citation
S. Lau, G. Jeffreys. "Kaehler Geometry of Quiver Varieties and Machine Learning." https://arxiv.org/abs/2101.11487 and get abstract from the link
Abstract
We develop an algebro-geometric formulation for neural networks in machine learning using the moduli space of framed quiver representations. We find natural Hermitian metrics on the universal bundles over the moduli which are compatible with the GIT quotient construction by the general linear group, and show that their Ricci curvatures give a Kahler metric on the moduli. Moreover, we use toric moment maps to construct activation functions, and prove the universal approximation theorem for the multi-variable activation function constructed from the complex projective space.
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This work is distributed under a Creative Commons Attribution 4.0 License.