Extremely Sparse Supervision Incentivizes Reasoning Ability

• URL: http://arxiv.org/abs/2609.04565v1
• Date: Thu, 03 Sep 2026 23:38:48 GMT
• Title: Extremely Sparse Supervision Incentivizes Reasoning Ability
• Abstract summary: Large language models demonstrate increasingly strong reasoning capabilities through effective post-training.<n> prevailing post-training methods optimize over massive numbers of tokens, implicitly assuming that effective learning must be token-intensive.<n>We discover a counter-intuitive phenomenon: reasoning can be effectively incentivized by an extremely small fraction of generated tokens.
• Score: 13.22207761303279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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