Most of the signal is already explained
A computational study of language-model activations, the internal signals produced as a model processes text, found that most of the apparent signal from swapping the order of two interventions was tied to the sites where those interventions entered the network. Across the reported family-by-configuration cells, a baseline built from single interventions accounted for 84.3% to 97.7% of the measured order-swap signal, with a mean of 93.7%. The first-order baseline accounted for none of the antisymmetrized second difference used as the corrected residual.
The raw measure compares two activation additions at distinct points inside a model, applied in one order and then the reverse. The researchers also recorded the four corresponding single-injection responses. Those responses form the no-fit baseline. Subtracting it from the order-swap bracket produces an antisymmetrized second difference that removes first-order effects and pure self-curvature terms to second order.
Testing covered six open-weight base model families in the 7 billion to 9 billion parameter range. The primary language-model evaluation used 16 trait contrasts, yielding 120 unordered pairs per family, and reused those pairs across three layer configurations. Directions came from two extraction seeds and disjoint prompt samples, with 48 held-out prompts used for evaluation. Direction agreement across seeds was imperfect: the mean cosine was 0.784, ranging from 0.667 to 0.833.
The correction leaves a smaller test
The plus/minus injection test gave the clearest warning about ordinary nonlinearity. In Llama and OLMo, the self-curvature component was 1.8 to 5.2 times the corrected residual at the primary configuration. Across all three configurations, it was 1.8 to 11.2 times larger. The result means that the response to an intervention on its own could exceed the remaining order-sensitive signal, even before asking whether that remainder represents a true mixed interaction.
One control used a prompt-split design intended to reduce prompt-level confounding by separating the prompts used to extract directions from those used to measure the effect. Under that design, three of the six families cleared the calibrated generic-interaction null: Llama at 1.599, OLMo at 2.059 and Qwen at 1.642, compared with a threshold of 1.324. The result was not uniform across the models tested.
A separate comparison changed the distance between the two intervention sites while matching the rest of the setup. The first-order share increased in the wider-separation condition for all six families and for 91.7% of 720 matched pairs. A same-shape untrained network moved in the predicted direction only 54% to 58% of the time. This pattern is consistent with site asymmetry as a major source of the raw signal, although the paper reports counts rather than a p-value because the family tests shared one trait inventory.
The strongest result is not universal
The scale test pointed in the same direction. As the intervention coefficient grew, the bracket followed a fitted scaling exponent between 0.886 and 1.043, close to first-order growth and far from the exponent of 2 expected for a pure bilinear interaction. The authors treat this as a diagnostic, not as proof that no learned interaction exists.
The pattern was also present in a random-init residual network, rather than only in trained language models. In a 16-layer network with width 768, baseline and bracket vectors had cosine agreement from 0.9956 to 0.9988 as the injection ratio ranged from 0.01 to 4. The weakest agreement occurred at 1, and the symmetric-control magnitude was 0.033. Because the trained-model norm ratio was not recorded for this comparison, it is not a matched test of trained and untrained systems.
Checks outside language models provided a limited portability signal. In released references, the corrected residual fell below a fixed Gaussian-direction null in 11 of 12 contrasts, including five of six for ViT-B/16 and all six for ResNet-50. The authors treated these results as portability checks, not as pooled evidence for the language-model findings.
The broad headline is narrower than the initial result. Within-pair analysis found the candidate effect at every configuration in only three families. Mistral did not clear the prompt-split test, leaving Llama and OLMo as the only families that survived every control. The paper therefore does not support a claim that all six model families share the same interaction.
A behavioral readout added a second boundary. It was designed to cancel additive contributions, and the corrected residual outperformed the raw bracket in four of six families. But the behavioral direction survived correction for multiple comparisons in only two of the six. That is a limited model-readout result, not evidence of a causal effect on people.
A measurement warning, not a general theory
Several limits remain. The finite-scale corrected residual still contains an uncontrolled higher-order remainder because empirical third-derivative bounds were not supplied, so it is not a pure interaction estimate. The plus/minus split was run only for Llama and OLMo, and the six families shared a single 16-trait inventory. Direction estimates were not perfectly stable across seeds, as the cosine range shows.
Data access also shapes what can be checked directly. The paper describes committed per-pair tensors, an independent CPU reference and raw held-out outputs, but the language-model single-injection responses behind an appendix are released only as scalar summaries. Some analyses therefore require rerunning forward passes. The document is an arXiv preprint, version 1, dated 26 August 2026.
For researchers measuring activation steering, the practical message is to record the four single-intervention responses before treating an order-swap measure as interaction. The study points to the corrected second difference as the more appropriate quantity, with the conclusion limited to distinct-site activation interventions. The surviving result remains family-dependent and layer-specific.
Paper data and sources
Original title: Activation-Space Order-Swap Geometry: A Site-Asymmetry Audit
Authors: Anqi Peter Li
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text