Title: Spurious Rewards: Rethinking Training Signals in RLVR
Primary area: foundation or frontier models, including LLMs
Keywords: reinforcement learning, large language model, reasoning model

Abstract: We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500
performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward),  13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting)---nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning---thinking in code without actual code execution---to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

TL;DR: We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer.