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This study investigates how language models execute in-context conditional rules by analyzing the mechanisms of testing predicates and routing answers using activation patching across multiple models and languages. The findings reveal that a mid-stack residual band effectively carries the truth value of predicates, allowing for high accuracy in rerouting answers, while the routing mechanism itself is found to be largely non-transferable and token-bound. Notably, the research demonstrates that while the testing module is modular, the routing module does not exhibit the same properties, highlighting critical differences in how language models process conditional logic.
Language models can reroute answers with near-perfect accuracy based on predicate truth values, but their routing mechanisms are surprisingly non-transferable across contexts.
When a language model follows an in-context conditional rule such as"if P(x) then A else B,"does it assemble a runtime circuit with one module that tests the predicate and another that routes the answer? We probe this with activation patching under a four-donor design whose two swapped-rule donors make the condition and the answer word disagree, so each layer reveals which of the two it carries. Across three open models from two families and six languages sharing one fixed item bank, a mid-stack residual band carries the predicate's truth value: patching it reroutes the answer with predicate-outcome flip near 1.0 and mapping flip near 0.0, meeting a strict pre-specified isolation criterion in 17 of 18 cells, and the same localization holds across five predicate families. The router shows the opposite profile. A learned subspace flips A and B near-perfectly within the trained pair yet transfers to a new pair at approximately 0 in every model, while in Gemma-3-4B (the only model probed cross-lingually) it transfers at approximately 0.98 to the same pair in other languages. Under every probe we ran, the router direction is token-bound and non-transferable (largely answer-readout in Gemma, pair-specific in Qwen) rather than an abstract routing module. Test is modular; under these probes, route is not.
