What question did this study set out to answer?

To formulate a multivector ontology for relational tables using Clifford algebra and empirically benchmark its numerical stability and tabular regression performance.

August 16, 2026Open Access

Clifford Tabular Algebra: A Multivector Data Model for Relational Tables, and the Measured Limits of Geometric Reformulation (A Rust Prototype, Part II) | wAI ~ wErrors

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AKArtiom KovnatskyWeatherford College

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Implication

Benchmarking study demonstrates that Clifford tabular algebra improves numerical precision and regression accuracy in relational data, highlighting multivectors for stable computation.

Key Points

To formulate a multivector ontology for relational tables using Clifford algebra and empirically benchmark its numerical stability and tabular regression performance.
Mapped columns to basis generators and rows to grade-1 multivectors in a dual-layer Rust prototype separating discrete semantics from numerical substrate.
Implemented an O(n d^2) closed-form algorithm for pairwise bivector energy and tested direct rectangular QR reduction against Gram matrix squaring.
Evaluated bivector-aware anisotropic regularization against isotropic Ridge regression across held-out tabular test splits.
Direct rectangular QR reduction achieved machine precision (< 10^-10) and outperformed Gram-based factorization on ill-conditioned features (residual 3.3 x 10^-9 vs. 1.1 x 10^-6).
Pairwise bivector energy computed in O(n d^2) rather than O(n^2 d^2), serving as an effective-rank statistic of the covariance spectrum.
Bivector-aware anisotropic regularization penalizing collinear directions consistently outperformed standard isotropic Ridge regression on held-out test splits.

Cite This Study

Artiom Kovnatsky (2026) studied this question.

synapsesocial.com/papers/6a8179eff2fb91fc834ad762 https://doi.org/10.5281/zenodo.21932856

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Implication

Benchmarking study demonstrates that Clifford tabular algebra improves numerical precision and regression accuracy in relational data, highlighting multivectors for stable computation.

Clifford Tabular Algebra: A Multivector Data Model for Relational Tables, and the Measured Limits of Geometric Reformulation (A Rust Prototype, Part II) | wAI ~ wErrors

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Cite This Study

Clifford Tabular Algebra: A Multivector Data Model for Relational Tables, and the Measured Limits of Geometric Reformulation (A Rust Prototype, Part II) | wAI ~ wErrors

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