clifra

clifra is a differentiable Clifford algebra computation layer for PyTorch. Signatures and grade layouts describe ordinary coefficient tensors; operations can be planned once and reused.

uv add clifra

import torch
from clifra import make_algebra

algebra = make_algebra(3, 0)
vectors = algebra.layout((1,))
product = algebra.plan_product(
    left=vectors,
    right=vectors,
    output=algebra.layout((0, 2)),
)

left = torch.randn(8, vectors.dim, requires_grad=True)
right = torch.randn(vectors.dim)
out = product(left, right)  # [8, 4]: scalar, e12, e13, e23
out.square().mean().backward()

The inputs store three vector coefficients each. The product broadcasts over the leading dimension and returns four scalar-and-bivector coefficients.

A signature defines basis products. A layout selects coefficient lanes, and a tensor contract declares compact or canonical storage. Planned operations fix these declarations while coefficient values and leading tensor dimensions remain ordinary PyTorch inputs.

Tutorials · How-to guides · Explanations · Research · API reference

Development

uv sync --group dev
uv run --group dev ruff check .
uv run --group dev pytest tests/ -n12 -q --tb=short
uv run --group docs mkdocs build

Please open an issue before proposing a substantial change. Contact: nemonanconcode@gmail.com.

Citation

@software{kim2026clifra,
  author  = {Kim, Eunkyum},
  title   = {clifra: Layout-first Clifford algebra tools for PyTorch},
  url     = {https://github.com/Concode0/clifra},
  version = {2.0.1},
  year    = {2026},
  doi     = {10.5281/zenodo.18939518},
  license = {Apache-2.0}
}

License

Apache License 2.0. See LICENSE and NOTICE.