# BARD: budget-aware reasoning distillation

arXiv: https://arxiv.org/abs/2511.01470 · HTML: https://mlsanity.com/paper/2511.01470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 15 of 15)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [ThinkDial: An Open Recipe for Controlling Reasoning Effort in Large Language Models](https://mlsanity.com/paper/2508.18773/) (2025)
- [Efficient Long CoT Reasoning in Small Language Models](https://mlsanity.com/paper/2505.18440/) (2025)

## Abstract (arXiv)

While long Chain-of-Thought (CoT) distillation effectively transfers reasoning capability to smaller language models, the reasoning process often remains redundant and computational budget uncontrollable, leading to inefficient resource usage. To address this limitation, we propose Budget-Aware Reasoning Distillation (BARD), a novel framework that simultaneously distills reasoning capability and enables fine-grained control over the reasoning length. BARD uses the thinking budget as a user-specified control signal, allowing the model to dynamically balance reasoning performance and computational efficiency. To achieve this concept, BARD introduces a two-phase training regimen. The first phase, Supervised Fine-Tuning (SFT) on teacher-generated long CoT data compressed to various budget levels, bootstrapping the model's understanding of budget constraints. The second phase leverages Reinforcement Learning (RL) from a reward signal in consideration of reasoning performance and budget fidelity simultaneously. Incorporating the two-phase regimen is crucial to avoiding policy degradation and ensuring that both objectives are optimized jointly. Extensive experiments demonstrate that our method empowers an 8B student model to achieve strong performance on challenging reasoning benchmarks (textitAIME24, AIME25, GPQA) while providing precise and adaptive control over its reasoning length across a wide range of budgets.