Active SAE Features Show Less Holonomy in Gemma 2B

This research investigates the distribution of "holonomy" – a measure of how a local frame rotates when carried around small loops in the residual stream – across active sparse autoencoder (SAE) feature planes in the Gemma 2 2B model. The study aimed to test the prediction that holonomy would concentrate on active feature planes, which is a concrete operationalization of the broader idea that semantic information is concentrated there. The experimental design, analysis, and verdict rules were preregistered to ensure rigor. Contrary to the initial prediction, the study found a reversal: active-feature planes carried *less* holonomy than matched mixed-feature controls. The adjusted log contrast was significantly negative, indicating a clear difference. This result falsifies the hypothesis that holonomy concentrates on active SAE feature planes in this specific model and measurement context. The paper emphasizes that this is an auditable operational reversal, not a causal claim that meaning suppresses holonomy. The underlying cause for this observed phenomenon remains an open question, with several alternative mechanisms suggested, including activation-strength geometry, degree of feature engagement, dictionary geometry, and transport distortion. The study highlights the importance of rigorous, preregistered methodologies in mechanistic interpretability research.