# Do Active SAE Feature Planes Carry More Holonomy? A Preregistered Reversal in Gemma

arXiv: https://arxiv.org/abs/2607.20522 · HTML: https://mlsanity.com/paper/2607.20522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 6 of its 7 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Gauge-invariant representation holonomy](https://mlsanity.com/paper/2601.21653/) (2026)

## Built on by (most cited first, 1 of 1)

- [Activation-Space Order-Swap Geometry: A Site-Asymmetry Audit](https://mlsanity.com/paper/2608.25315/) (2026)

## Abstract (arXiv)

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.