When Internalization Fails: Finding Better Targets for Reasoning Compression

Reasoning language models generate long reasoning traces that increase latency and cost. We study how to shorten these traces while preserving accuracy on competition-level mathematics. In a teacher-student distillation setup, we compare three approaches: (i) inference-time truncation after the first k tokens, (ii) Implicit Chain-of-Thought (ICoT)-style curricula that progressively shorten the teacher trace during training, and (iii) direct distillation to shorter reasoning traces. Using NUMINAMATH 1.5 with traces from DEEPSEEK-R1 and QWQ-32B, we distill into QWEN2.5-7B and measure accuracy against total tokens generated. We find: (1) with standard SFT and first-k truncation, models compensate by generating longer text after reasoning, undermining token savings; (2) ICoT-style curricula provide little benefit on competition-level mathematics, where reasoning traces are long and diverse; and (3) training on post-think, text the teacher generates after reasoning, achieves the best accuracy-efficiency trade-off among all shortened targets, outperforming generic summaries at matched token budgets. These results show that curriculum-based internalization methods effective on simple tasks do not transfer to complex reasoning, and that post-think provides a better distillation target.