Kaehler geometry of quiver varieties and machine learning
Lau, Siu-cheong; Jeffreys, George
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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