Activation-Space Order-Swap Geometry: A Site-Asymmetry Audit

• URL: http://arxiv.org/abs/2608.25315v1
• Date: Wed, 26 Aug 2026 02:54:02 GMT
• Title: Activation-Space Order-Swap Geometry: A Site-Asymmetry Audit
• Abstract summary: Order-dependent activation statistics are often interpreted as evidence of interaction, but that interpretation can be confounded by where interventions enter the network.<n>For a twice-differentiable readout, the open-path order-swap decomposes into a canonical additive response measured by single interventions.<n>Across six open-weight language-model families, the single-intervention baseline explains 84.3-97.7 percent of the bracket norm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Order-dependent activation statistics are often interpreted as evidence of interaction, but that interpretation can be confounded by where interventions enter the network. We introduce a no-fit site-asymmetry audit. For a twice-differentiable readout, the open-path order-swap decomposes into a canonical additive response measured by single interventions and an antisymmetrized second difference free of first-order and pure self-curvature terms to second order. Across six open-weight language-model families, the single-intervention baseline explains 84.3-97.7 percent of the bracket norm (mean 93.7 percent), while the no-interaction self-curvature term is 1.8-5.2 times larger than the corrected residual in the two families with the plus/minus injection split. The corrected residual clears a generic-interaction null in three of six families under a confound-free prompt split and two of six after configuration robustness. A known-positive surrogate recovers planted mixed interaction, while a matched site-separation test changes the baseline share and a random architecture reproduces the first-order regime. The same estimator transfers to released non-language references: trained residual fractions fall below a fixed Gaussian-direction null in 11/12 contrasts (5/6 ViT-B/16, 6/6 ResNet-50), a portability check rather than pooled evidence. The contribution is a reusable measurement criterion: run the single-intervention baseline before reading an order-swap vector as interaction or geometric structure; if it explains the vector, form the second difference instead. All claims are scoped to activation-space interventions at distinct sites; we do not claim that representation geometry is globally Abelian.

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