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  1. Book ; Online: Quantum Finite Automata and Quiver Algebras

    Jeffreys, George / Lau, Siu-Cheong

    2022  

    Abstract: We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified understanding towards ... ...

    Abstract We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified understanding towards quantum computing and deep learning. When the near-ring comes from a quiver, we have a nice moduli space of computing machines with metric that can be optimized by gradient descent.
    Keywords Computer Science - Formal Languages and Automata Theory ; Computer Science - Machine Learning ; Mathematics - Algebraic Geometry ; Quantum Physics
    Publishing date 2022-03-14
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Book ; Online: K\"ahler Geometry of Quiver Varieties and Machine Learning

    Jeffreys, George / Lau, Siu-Cheong

    2021  

    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 ... ...

    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 K\"ahler 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.

    Comment: v2: expanded on related works. 47 pages, 13 figures
    Keywords Mathematics - Algebraic Geometry ; Computer Science - Machine Learning
    Publishing date 2021-01-27
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

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