When a large language model (LLM, a text-predicting program) gives an answer, it usually writes reasoning steps first. Standard training rewards only whether that answer is right, so the reasoning can become irrelevant decoration. Then the model's logic is hard to trust.
The authors add a reward based on scrambling the order of those steps without changing their content. If the final answer becomes less likely after scrambling, the reasoning actually mattered, and the model is rewarded.
This raised accuracy on unseen logic and game problems to 46.8%, beating the strongest comparison method. It also made reasoning more faithful: when a hint was present, models acknowledged it 34.0% of the time, far more often than the comparison. Trustworthy reasoning matters for real decisions.
