Represented But Not Composed: How Numerical Comparisons Enter Language-Model Decisions

We show that a language model can represent a rule's numerical comparison without that representation causally controlling the verdict. We test this across four instruction-tuned models (Llama, Qwen, Gemma, Mistral) in two controlled rule-following settings. In a simple US Federal Aviation Administration (FAA) altitude rule, changing the stated ceiling strongly changes the verdict in the three models with a sufficiently strong FAA decision signal. In a more complex anti-structuring rule, where an amount–threshold comparison must combine with how the transaction is split, changing the threshold barely changes the verdict even when only one comparison changes. We contrast this numerical comparison with rule polarity (whether the rule permits or prohibits the action). This is not a representation failure: threshold-dependent information reaches the decision layer even when the gold answer is held fixed. In Llama, this representation is graded and causally movable, yet moving it across the threshold shifts the verdict by only 2.0–2.3% of the polarity-control effect; the identical intervention on the polarity decision direction serves as a positive control and flips the verdict completely. Across all four models, the late-layer components that drive the decision respond strongly to qualitative action structure but negligibly to the stated threshold. The same dissociation appears behaviorally: in Llama, telling the model that the full amount is below the threshold repairs 0 of 115 over-flagged cases, while telling it the resulting qualitative judgment that the split does not evade reporting repairs 115 of 115. Gemma matches this exactly; Qwen shows the same asymmetry less completely; Mistral shows partial repair. The numerical comparison is represented, graded, and causally movable, yet barely controls the verdict in this task: it is represented but not composed.