DeepSeek-style reasoning distillation: what travels from teacher to student, and what gets cut from the loss?

**The teacher does more than answer.** A strong reasoning model is prompted on hard problems and produces a full step by step reasoning trace, followed by a final answer. Both parts go into the training data. Each example for the student is a triple of (problem, trace, answer). When you format it as a single sequence for SFT, the problem is the prompt and the trace plus answer together are the response. The loss is standard completion-only cross-entropy. Prompt tokens are masked with -100 so they do not contribute to the gradient. Trace and answer tokens are kept inside the loss. The student is graded on reproducing the teacher's full working, not just the bottom line. If you drop the trace and supervise on (problem, answer) pairs, the student learns to map problems to answers on the training distribution and not much else. The procedure that produces those answers is missing from the signal, so the student cannot generalise to a new problem. The trace is what carries the reasoning ability across.

**The teacher produces traces, not just answers.** A strong reasoning model, prompted on hard problems, emits a full chain-of-thought followed by a final answer. Each training example becomes a (problem, trace, answer) triple, formatted as one sequence in the chat template: the problem sits in the prompt span, the trace plus answer sits in the response span. The loss is completion-only SFT cross-entropy. Prompt tokens are masked with the ignore_index of -100. Trace tokens and final answer tokens are kept in the loss. The student is graded on producing the same reasoning trajectory the teacher used, token by token. Quality control usually filters by correctness. Only traces whose final answer matches the gold answer are kept; the rest are dropped or rejection-sampled. Some recipes also reweight examples or run a brief preference-tuning pass on top, but the core SFT step is the load-bearing one. Dropping the trace collapses the recipe. With (problem, answer) supervision alone, the student learns a shallow mapping from problems to answers on the training distribution. The procedure that produced those answers is invisible to it. A held-out problem looks new, and there is no learned reasoning template to apply. You end up with a model that memorises a fixed set of answers rather than one that has absorbed the teacher's reasoning ability.