From Explicit Holonomy to Latent Control Fields

In prior work, we introduced the Holonomy Transformer (HoT), an architecture that enforces reasoning consistency through explicit geometric constraints derived from differential geometry. While conceptually principled, the original formulation incurs substantial computational overhead due to dense, pairwise holonomy computation.

In this paper, we present a counter-argument to the necessity of explicit holonomy measurement and introduce an alternative formulation based on a latent, predictive control field. Rather than measuring inconsistency after it manifests, the proposed approach learns to anticipate inconsistency locally and gate information flow accordingly.

This reformulation preserves the inductive bias toward consistent reasoning while reducing computational complexity by more than an order of magnitude, making consistency-aware architectures plausible at scale. The paper serves both as a self-critique of the original formulation and as a principled path toward efficient implementation.