Didactic to constructive: Turning expert solutions into learnable reasoning

Improving the reasoning capabilities of large language models (LLMs) typically relies either on the model's ability to sample a correct solution to be reinforced or the existence of a stronger model able to solve the problem. However, many difficult problems remain intractable for even current frontier models, preventing the extraction of valid training signals. A promising alternative is to leverage high-quality expert human solutions, yet naive imitation of this data fails because it is fundamentally out-of-distribution: expert solutions are typically didactic, containing implicit reasoning gaps intended for human readers rather than computational models. Furthermore, high-quality expert solutions are expensive, necessitating generalizable, sample-efficient training methods. We propose Distribution Aligned Imitation Learning (DAIL), a two-step self-distillation method that bridges the distributional gap by first transforming expert solutions into detailed, in-distribution reasoning traces and then applying a contrastive objective to focus learning on expert insights and methodologies. We find that DAIL can leverage fewer than 1000 high-quality expert solutions to achieve up to 31% pass@128 gains on Qwen2.5-Instruct and Qwen3, double reasoning efficiency, and enable out-of-domain generalization.