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The proposed DAIL method addresses the out-of-distribution challenge of training on expert human solutions by converting didactic explanations into computational reasoning traces via self-distillation. This approach achieves significant efficiency gains, requiring fewer than 1,000 expert examples to double reasoning efficiency while enabling out-of-domain generalization. For researchers, this offers a sample-efficient pathway to improve LLM reasoning without relying on stronger models or intractable problem instances.
Making Expert Reasoning Learnable with Self-Distillation
arXiv:2602.02405v2 Announce Type: replace Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2602.02405 [cs.LG]
(or arXiv:2602.02405v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.02405 Focus to learn more arXiv-issued DOI via DataCite
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