Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models

This paper studies a common repair strategy for reasoning distillation: showing a chain-of-thought generator the gold answer and asking it to produce a derivation reaching that answer. In a controlled experiment, answer-conditioned chains increasingly rationalize backward from the target instead of deriving it. Correctness filtering fails to detect the damage because the final answer is correct. Fine-tuning a strong instruction-tuned reasoning model on its own conditioned chains reduces verifiable-reasoning accuracy, with losses reaching about 27 points on the hardest competition problems. The effect is visible before training, transfers across teacher families, and is attributed to the rationalize-toward instruction rather than answer visibility alone.