Large language models demonstrate strong reasoning capabilities through post-training. Conventional methods optimize over many tokens, but this study revisits the assumption that token-intensive learning is necessary.
Using the Qwen3 family, the researchers found that extremely sparse supervision—just one or two tokens per reasoning trajectory—can effectively incentivize reasoning. This corresponds to only 0.05% of all tokens and often matches or exceeds the performance of full-token training.
The phenomenon was observed across nine different teacher--student configurations, model scales, and tasks including mathematical and coding reasoning. It was also validated on models like Llama and reinforcement learning with verifiable reward.
This suggests that effective post-training may not require token-intensive methods. Instead, focusing on critical reasoning steps and minimal updates could be more efficient, aligning with natural learning processes.
Source: https://arxiv.org/abs/2609.04565