# Extremely Sparse Supervision Incentivizes Reasoning Ability

arXiv: https://arxiv.org/abs/2609.04565 · HTML: https://mlsanity.com/paper/2609.04565/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [TIP: Token Importance in On-Policy Distillation](https://mlsanity.com/paper/2604.14084/) (2026)

## Built on by (most cited first, 5 of 5)

- [1% of Tokens Can Be Enough: On Gradient Estimation in On-Policy Distillation](https://mlsanity.com/paper/2609.24432/) (2026)
- [Dr. OPD: Learning What to Follow for Optimal On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2609.38025/) (2026)
- [DIAL-OPD: Learning More from Fewer Tokens in On-Policy Distillation](https://mlsanity.com/paper/2610.11659/) (2026)
- [Collaborative Learning and Reasoning over Model Slices](https://mlsanity.com/paper/2610.12927/) (2026)
- [OPMD: On-Policy Mechanism Distillation Beyond Output Supervision](https://mlsanity.com/paper/2610.14022/) (2026)

## Abstract (arXiv)

Large language models demonstrate increasingly strong reasoning capabilities through effective post-training. Yet, prevailing post-training methods optimize over massive numbers of tokens, implicitly assuming that effective learning must be token-intensive. We revisit this assumption in the on-policy distillation (OPD) setting, which naturally admits dense teacher supervision at every generated token. Using the Qwen3 family, we discover a counter-intuitive phenomenon: reasoning can be effectively incentivized by an extremely small fraction of generated tokens--as few as one or two tokens per reasoning trajectory, corresponding to only 0.05% of all tokens. Surprisingly, this sparse supervision in most cases matches or surpasses full-token training in improving reasoning ability, despite excluding the vast majority of generated tokens from the training objective. This phenomenon is consistently observed across nine teacher--student configurations spanning different model scales on mathematical reasoning tasks, and is further validated on coding reasoning, Llama models and Proximal Policy Optimization (PPO)-based reinforcement learning with verifiable reward (RLVR). Interestingly, such extremely sparse supervision may be closer to the natural learning process: rather than correcting every step word by word, one reflects on a few critical reasoning steps, updates prior understanding, and continues the trial-and-error, avoiding micro-level corrections while remaining remarkably effective. Overall, our results challenge the assumption that effective post-training must be token-intensive and point to a new direction for understanding and designing more efficient post-training algorithms.