---
title: "GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity — Stuff That Spins"
description: "arXiv:2607.00152v1 Announce Type: new 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 i…"
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keywords: ["SpinGraph", "spin analysis", "GEO"]
date: "2026-07-02T04:00:00+00:00"
modified: "2026-07-02T16:51:20.469748+00:00"
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# GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity

**Source:** Unknown  
**Published:** July 2, 2026  
**Original:** https://arxiv.org/abs/2607.00152  

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