Distribution Corrected Offline Data Distillation for Large Language Models

TL;DR

This paper introduces a new offline reasoning distillation framework for large language models that corrects distributional drift, leading to improved reasoning accuracy and more stable traces without requiring online sampling.

Contribution

It proposes a principled, distribution-correction-aware offline distillation method that enhances reasoning performance and stability in large language models.

Findings

Improves reasoning accuracy on GSM8K, MATH, MATH500, AMC, AIME, and OlympiadBench.

Produces more stable reasoning traces compared to prior offline algorithms.

Maintains instruction-following capabilities while strengthening reasoning.

Abstract

Distilling reasoning traces from strong large language models into smaller ones is a promising route to improve intelligence in resource-constrained settings. Existing approaches face a fundamental trade-off: offline distillation from teacher-generated traces provides high-quality, sample-efficient supervision but suffers from distributional drift: during training, the student model conditions on teacher-generated prefixes, whereas during inference the student autoregresses on self-generated prefixes, leading to compounding errors over long reasoning trajectories. Meanwhile, on-policy or self-distillation methods better match the student's inference-time distribution, but require costly online sampling and often produce low-quality traces in early training. We propose a principled offline reasoning distillation framework that preserves the efficiency and supervision quality of offline teacher-generated data while correcting teacher-student distribution drift. It adaptively emphasizes teacher supervision that is better aligned with the student's on-policy distribution. Evaluations on mathematical reasoning benchmarks of GSM8K, MATH, MATH500, and harder held-out competition-style tasks, including AMC, AIME, and OlympiadBench, show that our method improves reasoning accuracy over prior offline distillation algorithms and yields more stable reasoning traces while preserving instruction-following capabilities. Our work shows that lightweight, distribution-correction-aware training can substantially strengthen offline reasoning distillation without online rollouts.