clifra

Layout-first Clifford algebra tools for PyTorch.

A clifra algebra host owns its layouts, policies, and operation plans. Full-lane tensors and compact grade layouts share that algebra, while planning builds static executors for products, metrics, exponentials, and actions. Layers and other library components reuse the same operations.

Install

uv sync
uv sync --extra dev

Docs:

uv sync --group docs
uv run --group docs mkdocs serve

Minimal Use

import torch

from clifra import make_algebra

algebra = make_algebra(3, 0, device="cpu")
vectors = algebra.layout((1,))
products = algebra.plan_product(
    op="gp",
    left_layout=vectors,
    right_layout=vectors,
    output_layout=algebra.layout((0, 2)),
)

left = torch.randn(8, vectors.dim)
right = torch.randn(8, vectors.dim)
out = products(left, right)

Checks

uv run pytest tests/ -m unit -q --tb=short
uv run pytest tests/ -m "not slow" -q --tb=short
uv run ruff check .
uv run --group docs mkdocs build

See the documentation for tutorials, explanations, benchmarks, and the generated API reference.

Research

research/continuum_solver is one repository-local system built on clifra. It uses clifra charts, bivector fields, and planned algebra operations to study continuum deformations. It is an example of the library's use as research infrastructure, not a definition of clifra's scope.

Contribution

Found a problem or want to propose a change? Please open an Issue first, especially before a PR, so the scope is clear.

For direct contact, email: nemonanconcode@gmail.com

License

Apache License 2.0. See LICENSE and NOTICE.

Citation

@software{kim2026clifra,
  author  = {Kim, Eunkyum},
  title   = {clifra: Clifford Algebra Layers for PyTorch},
  url     = {https://github.com/Concode0/clifra},
  version = {1.2.0},
  year    = {2026},
  doi     = {10.5281/zenodo.18939518},
  license = {Apache-2.0}
}

References

RotorGadget Background

The following paper is background reference material for RotorGadget. It is not maintained as a normative implementation specification, and its inclusion does not claim strict reproduction or conformance:

• Pence, T., Yamada, D., & Singh, V. (2025). "Composing Linear Layers from Irreducibles." arXiv:2507.11688.

Optimization Background

The tag-aware optimizers in clifra/optimizers/ dispatch spin, sphere, and euclidean post-update handling. The following books are background references, not normative specifications for those implementations:

• Absil, P.-A., Mahony, R., & Sepulchre, R. (2008). Optimization Algorithms on Matrix Manifolds. Princeton University Press.
• Boumal, N. (2023). An Introduction to Optimization on Smooth Manifolds. Cambridge University Press.