Consistency Is All You Need: Anticipatory Control Fields for Transformer Architectures

Consistency Is All You Need

Linear-Complexity Geometric Consistency for Transformer Architectures via Anticipatory Control Fields

This record contains the full paper Consistency Is All You Need and accompanying implementation of the Control Field Holonomy Transformer (CF-HoT), a Transformer architecture that introduces consistency as a first-class architectural bias rather than an emergent or post-hoc property.

The central contribution of this work is a reframing of consistency from a measurement problem to an anticipation problem. Instead of explicitly computing pairwise inconsistencies (e.g., via holonomy or loop-based geometric comparisons, which are computationally prohibitive), the architecture learns to predict and accumulate a scalar proxy for future inconsistency during generation. This signal—called a control field—is then used to softly gate attention and feedforward computation in a causal, differentiable manner.

Although inspired by concepts from differential geometry (fiber bundles, parallel transport, holonomy, curvature), the implementation deliberately does not perform rigorous geometric computation. Rather, geometric language is used as a conceptual framework motivating a practical, learned approximation that reduces consistency-related computation from prohibitive O(n²·d³) formulations to O(n) per layer, while retaining standard Transformer attention costs.

This release includes:

• The full paper Consistency Is All You Need

• A complete PyTorch implementation of CF-HoT

• Training scripts demonstrating stable end-to-end optimization

• Empirical validation of trainability, numerical stability, and bounded overhead on synthetic data

Scope and limitations:
This work demonstrates architectural feasibility and trainability only. It does not yet evaluate improvements in semantic consistency, factual correctness, or reasoning performance on downstream benchmarks. Such evaluations are explicitly identified as future work. The control field should therefore be understood as a learned regularization and routing mechanism, not a verified consistency detector.

The paper is intended to be read as:

• a systems and architecture contribution,

• a proposal for treating consistency as an architectural primitive, and

• a foundation for future empirical and alignment-oriented investigation.

Feedback, critique, and empirical extensions—particularly evaluations on reasoning and contradiction benchmarks—are encouraged.