mlsanityData to 7 Oct 2026

Noncommutative Geometry of Computational Models and Uniformization for Framed Quiver Varieties

arXiv 2201.05900 ↗First posted 15 Jan 2022math.AG cs.LG math.SGcited by 2

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Abstract (arXiv)

We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find moduli of Euclidean and non-compact types in light of uniformization.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 29 references that are in the map. First posted on arXiv 15 Jan 2022.

Builds on

12 of 29 references.

References · 12

  1. 2016Group Equivariant Convolutional Networkscited by 1,154
  2. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  3. 2018Spherical CNNscited by 452
  4. 2018Hyperbolic Neural Networkscited by 393
  5. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  6. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  7. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 204
  8. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 160
  9. 2020The Representation Theory of Neural Networkscited by 18
  10. 2019Covariance in Physics and Convolutional Neural Networkscited by 12
  11. 2021Categorical Representation Learning: Morphism is All You Needcited by 6
  12. 2021K"ahler Geometry of Quiver Varieties and Machine Learningcited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 1.

2 papers.

  1. 2024A logifold structure on measure spacecited by 2
  2. 2022Quantum Finite Automata and Quiver Algebrascited by 0