Consistency Training Suppresses Cue Following Without Teaching Cue Selectivity

Language models often change answers because of a cue, a hint such as "I believe the answer is B" that gives no valid evidence. Consistency training (CT) trains a model to answer the same with and without the cue. Four CT methods apply this idea to output tokens (BCT), residual activations (ACT), attention patterns (AttCT) and sampled-answer rates (RMCT). Prior work suggests some learn different solutions. We train all four on Gemma-2-2B-it and Llama-3.1-8B-Instruct with the same data. We test predictions written in advance and inspect the models with a known circuit that carries cues to the answer. All four make the trained cue less effective, and their fixes share three properties. First, correct cues lose about as much influence as wrong ones. Second, the fix is usually large for cues before the answer options, as in training, and much smaller after them. Llama RMCT depends least on position. Third, the circuit heads still carry most remaining cue-induced errors. Making BCT targets depend on the cue's correctness mostly weakens the fix. CT thus weakens the trained cue without teaching models when a cue is right. Evaluations with only wrong cues at the trained position miss the first two properties.