Are Dense Rewards Worth Their Tokens in GRPO?

RLVR trains language models to reason by rewarding correct final answers. A widely used algorithm, group- relative policy optimization (GRPO), gives every token of a solution the same credit, so dense process rewards have been proposed to credit intermediate steps, for example with a Monte-Carlo reward that scores each step by sampling continuations from it. Comparing such a reward with GRPO per training update, or vetting it with a gradient test on a single batch, leaves out what it costs: in our setting, the continuations alone take 91% of all generated tokens. We introduce a matched-compute protocol that gives every training intervention the same budget, measured in both generated tokens and training GPU-hours, and tests it in preregistered studies with controls for side effects. Across 1,668 runs on six models, we find that matching compute reverses the ranking. On Qwen2.5-1.5B, the Monte-Carlo reward leads standard GRPO per update, yet ends 14.3 percentage points lower at equal tokens and 7.8 points lower at equal training time, and none of four dense-reward variants outperforms GRPO even when given as much training time. A per-token gradient test orders these rewards as training does but overestimates each by one to two points, as much as the gains it is meant to detect. In contrast, training on the prompts whose predicted success is nearest 1/2 improves accuracy at matched compute, by 1.7 points on Qwen3-0.6B and 0.8 on Qwen2.5-1.5B. These gains replicate on fresh seeds and unseen problems, and a simple rule, that the candidate prompts are predicted to fail more often than not, predicted where they appear in five of six preregistered tests. The protocol also measures what such gains are worth: they come early in training, and standard GRPO with twice the initial learning rate comes within half a point of them. We argue that training interventions should be validated at matched compute, which overturns some apparent gains and confirms others.