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From Explicit Holonomy to Latent Control Fields

Authors: Napolitano, Logan Matthew;

From Explicit Holonomy to Latent Control Fields

Abstract

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green