MS-TTRL: Breaking the Frequency Conflict in Multiple-Solution Test-Time Reinforcement Learning

Zhixia Zhang, Binqian Xu, Huaiyang Wang, Yikun Ban, Dianbo Liu

Scientific, engineering, and mathematical reasoning tasks can admit multiple valid solutions, while exhaustive annotation of the full solution set is often prohibitively costly. Test-time reinforcement learning (TTRL) applies reinforcement learning to unlabeled test instances, offering a label-free approach to multiple-solution reasoning. In this setting, generation frequency serves two opposing objectives: correctness estimation favors frequent outcomes, whereas outcome-level diversity preservation favors less frequent outcomes. We term this tension the \textbf{Frequency Conflict}. To resolve this conflict, we propose MS-TTRL, which obtains frequency-independent correctness estimates through Outcome-Level Self-Verification while reserving generation frequency solely for diversity preservation. Three-State Outcome Cache and the Candidate State support verification reuse across repeated observations and confidence-aware handling of ambiguous outcomes, while Confidence-Gated Inverse Probability Scaling selectively strengthens the learning signals of rare, reliably verified outcomes. Experiments across two benchmarks, four multiple-solution tasks, and three backbone models, each…