GA for NNs

Geometric Algebra for Neural Networks: A Survey

Tao Zhong1, Kaison Fong2, Keqin Wang1, Christine Allen-Blanchette1

1Princeton University 2Stanford University

Paper arXiv PDF GitHub

Abstract

    Positioning diagram: broad GDL surveys, domain-specific GDL surveys and general GA surveys versus this survey, which is GA-native and deep, covering foundations, equivariance, architectures, applications, empirical evidence and software.

    Which algebra fits your task?

    Pick the need that best describes your data. The recommendation, its rationale and the conditions to avoid it come straight from the survey’s algebra-selection guide (§II-D, Table 2).

    Primary task need

    Paper explorer

    Every work the survey cites, tagged by where it is discussed. Filter by topic, algebra and year, or search titles, authors and model names. Each entry quotes the sentence the survey uses to place it.

    Cited works per year in the current selection. Click a bar to filter that year.

      Architecture families

      GA-native networks reuse a small set of primitives (grade projections, geometric products, versor actions, inner-product attention) and combine them into six families (§IV, Table 5). Open a family to see its representative works in the explorer.

      Canonical design motifs in GA-native architectures, showing how families combine shared GA primitives.

      How each algebra encodes geometry

      What the evidence supports

      Results are compared only within matched benchmark settings (§VI, Table 7). No setting yet reaches “Strong” by archival-survey standards.

      When is GA worth it?

      Equivariant paradigms compared along the dimensions that matter for architecture selection (§III-D, Table 3). GA-native networks are the only paradigm with native support for both mixed geometric entities and join/meet operations; mature non-GA methods remain the stronger default when the symmetry and data type are already well matched.

      Recommended benchmarking practice

        Software

        Libraries for multivectors and Clifford operations (§VII, Table 8). Only the first group offers native deep-learning tensor support; the rest serve preprocessing, prototyping or performance-critical kernels.

        Figures

        Cite

        If the survey or this explorer helps your work, please cite:

        @article{zhong2026geometric,
  title   = {Geometric Algebra for Neural Networks: A Survey},
  author  = {Zhong, Tao and Fong, Kaison and Wang, Keqin and
             Allen-Blanchette, Christine},
  journal = {arXiv preprint arXiv:2610.30121},
  year    = {2026},
  url     = {https://arxiv.org/abs/2610.30121}
}

        Add a paper

        Missed a GA-native network, or published a new one? This page doubles as an awesome-list, and pull requests are welcome.

        1. Fork the repository.
        2. Append an entry to data/community.json with a title, authors, year, venue, link, and the algebra if it is GA-native.
        3. Run python3 scripts/build_readme.py to refresh the README list, then open a pull request.

        Community additions appear in the explorer with a “community” mark until they are reviewed for the next survey revision. Corrections to survey entries are best sent as an issue.