The Holonomy Transformer: A Geometrically-Native Neural Architecture for Consistent Reasoning

This work introduces the Holonomy Transformer (HoT), a neural architecture that embeds geometric consistency constraints directly into transformer computation. Tokens are represented as sections of a fiber bundle, and attention is computed via parallel transport with holonomy-based costs that structurally suppress inconsistent information flow.

The architecture enforces reasoning consistency as a geometric property rather than a learned statistical regularity, using holonomy penalties, curvature-gated feedforward layers, and waypoint-based routing. A companion technical report describes extensions in which creativity and exploration are treated as cost-guided deviations within the learned geometric manifold.

This submission presents the core architecture and theoretical framework. Empirical scaling and benchmarking are left to future work.