clifra

clifra is a differentiable Clifford algebra computation layer for PyTorch. Signatures and layouts give tensor coefficients their mathematical meaning. Operations act on those tensors directly or can be planned for reuse.

A vector in \(Cl(3,0)\) has three coefficients. Its geometric product with another vector has a scalar part and a bivector part:

import torch
from clifra import make_algebra

algebra = make_algebra(3, 0)
vectors = algebra.layout((1,))

a = torch.tensor([1.0, 0.0, 0.0])
b = torch.tensor([0.0, 1.0, 0.0])

ab = algebra.geometric_product(a, b, left=vectors, right=vectors)
# [0, 1, 0, 0]: coefficients of 1, e12, e13, e23

The final axis holds coefficients in the declared layout. Leading dimensions broadcast as ordinary PyTorch dimensions; autograd differentiates the executed tensor operations.

Computation model

clifra keeps coefficient data in ordinary PyTorch tensors.

Layouts describe the algebraic meaning of the final coefficient axis without changing PyTorch's ownership of leading dimensions, devices, dtypes, or autograd.

Operations can be executed directly or planned from algebraic structure and reused across changing tensor values and batch shapes.

The same model applies across Euclidean, projective, conformal, and indefinite Clifford algebras.

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The tutorials introduce coefficient tensors, layouts, broadcasting, and planned differentiation, followed by geometric applications. The how-to guides cover individual tasks, including strict blade geometry, resource budgets, compilation, and executor extensions.

The explanations develop representation, products, signed forms, numerical behavior, and execution semantics.

The research notes show how the same computational model is used in geometric optimization and transformation-field experiments.

The API reference documents the stable public interfaces.