Versor: A Geometric Sequence Architecture
Truong Minh Huy, Edward Hirst

TL;DR
Versor introduces a geometric sequence architecture using Conformal Geometric Algebra, achieving superior performance, interpretability, and efficiency across diverse tasks compared to traditional neural network models.
Contribution
The paper presents Versor, a novel geometric sequence architecture leveraging CGA for improved generalization, interpretability, and efficiency, with new mechanisms like RRA and GPA for scalable relational modeling.
Findings
Outperforms Transformers and GNNs on multiple benchmarks
Uses significantly fewer parameters (up to 200x less)
Maintains stable out-of-distribution predictions
Abstract
A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and significant performance improvements on a variety of tasks, while offering improved interpretability and efficiency. By embedding states in the manifold and evolving them via geometric transformations (rotors), Versor natively represents -equivariant relationships without requiring explicit structural encoding. Versor is validated on chaotic N-body dynamics, topological reasoning, and standard multimodal benchmarks (CIFAR-10, WikiText-103), consistently outperforming Transformers, Graph Networks, and geometric baselines (GATr, EGNN). Key results include: orders-of-magnitude fewer parameters ( vs. Transformers); interpretable attention decomposing into proximity and orientational…
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Machine Learning in Materials Science · Topological and Geometric Data Analysis
