[Submitted on 9 Jul 2026]
Title:Do Active SAE Feature Planes Carry More Holonomy? A Preregistered Reversal in Gemma
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Abstract:This paper tests whether holonomy concentrates on active sparse-autoencoder (SAE) feature planes in Gemma 2 2B, a concrete operationalization of the broader semantic-concentration prediction. Holonomy is measured at the final-token layer-12 to layer-13 residual-stream readout by carrying a local frame around small loops using the instrument's restricted-Jacobian transport rule, then normalizing the resulting rotation by enclosed area. The design, materiality threshold, analysis, and verdict rules were preregistered and frozen before the analysed measurements were inspected. The prediction was falsified in reverse: active-feature planes carried less holonomy than matched mixed-feature controls, with an adjusted log contrast of -0.29439 and 95% interval [-0.43989, -0.14889]. A magnitude-only explanation was not supported in this design, while the three-way ordering across random, mixed-feature, and active-feature planes was undefined at matched magnitude because common support failed. Post-freeze diagnostics at the same readout supported the area law on a small validation subset, bounded matched-center displacement under a simple paired regression, and identified transport distortion as a live mechanism or confound. The result is therefore a narrow, auditable operational reversal, not a causal claim that meaning suppresses holonomy. The cause remains open, with activation-strength geometry, degree of feature engagement, dictionary geometry, matched-center displacement, activation-manifold proximity, and transport shear as live alternatives.
Comments: 23 pages, 5 figures. Preregistered confirmatory study; frozen experiment record archived at Zenodo, doi:https://doi.org/10.5281/zenodo.20960027
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2607.20522 [cs.LG]
(or arXiv:2607.20522v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.20522
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Larry Richards [view email] [v1] Thu, 9 Jul 2026 05:04:25 UTC (48 KB)
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