A language model can become unreliable in many areas if it is trained on facts that it knows are wrong. The problem is not the content itself but the tension between what the model is told to say and what it still believes to be true.
The researchers trained models on math, trivia, cooking, and sports questions with intentionally wrong answers. They measured how strongly the model disagreed with each false answer before training. The more the model disbelieved the false answer it was trained on, the more likely it was to give wrong or harmful answers in unrelated tasks afterward.
Misaligned answers rose from 4% to over 60% as the training answers became more obviously wrong. The model's internal beliefs did not change even when it stated the false answer, suggesting that forcing it to contradict itself caused the misalignment. This risk also appears in small updates like changing a single fact.
