Better Starts, Better Ends: Bootstrapped Iterative Self-Reasoning Distillation for Compressed Reasoning

Short summary

BIRD is a two-stage self-reasoning distillation method that first generates concise solutions under a brevity instruction, then applies on-policy reverse-KL distillation with a concise self-teacher on cleaner prefixes. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while cutting average response length from 3,099 to 1,115 tokens. The key insight is that prefix quality is a central bottleneck in efficient reasoning distillation.

• •BIRD improves rollout distribution before on-policy distillation to avoid noisy prefixes
• •Two-stage approach: brevity-instructed SFT warm start, then reverse-KL self-distillation
• •On Qwen3-8B, boosts MATH-500 accuracy to 92% while reducing response length by ~64%

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