arXiv Machine Learning October 12, 2026 By Alex Guerra, Joshua Aduol, Yaqian Tang, Daniel Williams, Ryan P. Adams, Peter Orbanz

Coordinate-Free Automatic Differentiation

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The paper introduces a basis‑independent derivative operator that can represent a wide range of geometric differential operations, such as rotations, volume forms, and curvatures, without requiring explicit coordinate arrays. This operator is built solely from existing automatic differentiation primitives and can be composed with JAX’s batching, compilation, and hardware acceleration features. The authors demonstrate its reusability across manifold operators, its integration into a spacetime inverse‑problem pipeline, and its application to optimization over rotor subgroups.

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