GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity

arXiv:2607.00152v1 Announce Type: cross Abstract: Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization