Prompt Dominance and Asymmetric Verifier Costs: Empirical Ablations of GRPO at 1B Scale on GSM8K

Abstract:This paper studies GRPO at 1B scale from both directions: what estimator choices do to the learning signal, and what a degraded reward signal does to what is learned. We train OLMo-2-0425-1B on GSM8K with a from-scratch implementation and measure both sides in controlled sweeps, including a verifier-quality experiment that degrades the training reward and the test-time selector identically. Four results stand out. The prompt is the first-order decision: the zero-shot prompt leaves the base model at 0.08% (its outputs are degenerate continuations, not wrong answers), so almost no group carries a gradient, and training succeeds because the 3-shot prompt reaches 18.3%. At this scale the estimator variants sit within seed noise, with Dr. GRPO ahead on both seeds. In the off-policy regime, clipping is the whole story: training on data without a clipped ratio loses 4-6 points relative to the on-policy reference, while GRPO-style clipping and GSPO recover the loss entirely. Finally, the same weak verifier is far cheaper in RL than in test-time selection: a 10%-flip verifier leaves RL's attainable gain intact (91% and 106% retained across two seeds) where selection retains 57%, and a format-only verifier leaves RL with 16-30% of its gain and selection with essentially nothing. Flip noise acts as an affine transform on the expected reward, and the group-normalized advantage with Adam's rescaling removes it exactly; the residual is a second-order variance effect that the matched-step comparison at a 30% flip rate tests.

12 pages, 8 figures. Code, run records, and figure scripts: this https URL

Machine Learning (cs.LG)

arXiv:2610.04928 [cs.LG]

(or arXiv:2610.04928v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.04928 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.