Quantum Finite Automata and Quiver Algebras
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 12 of its 32 references that are in the map. First posted on arXiv 15 Mar 2022.
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12 of 32 references.
References · 12
- 2016Group Equivariant Convolutional Networkscited by 1,154
- 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
- 2018Spherical CNNscited by 452
- 2018Hyperbolic Neural Networkscited by 393
- 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
- 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
- 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 204
- 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 160
- 2020The Representation Theory of Neural Networkscited by 18
- 2019Covariance in Physics and Convolutional Neural Networkscited by 12
- 2021K"ahler Geometry of Quiver Varieties and Machine Learningcited by 3
- 2022Noncommutative Geometry of Computational Models and Uniformization for Framed Quiver Varietiescited by 2
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