CoRE: Consensus Rewards via Equilibrium for Test-Time Reinforcement Learning

On unlabeled test data, reinforcement learning lacks a ground-truth reward; test-time RL methods derive one from the model's own roll-outs, rewarding those that match the majority vote over N sampled answers. That vote discards a correct answer whenever it is a minority and scores every majority-matching roll-out identically. We replace it with CoRE (Consensus Rewards via Equilibrium): the N roll-outs form a graph whose edges combine answer agreement, reasoning similarity, and generation confidence, and replicator dynamics extract its dominant set, yielding a refined pseudo-label, a graded per-roll-out reward, and a per-question cohesiveness gate. CoRE strictly generalizes voting: majority voting is recovered as a special case; a block-value analysis gives a sharp threshold for when consensus recovers a correct minority against a larger wrong plurality; and confidence calibration provably lowers that threshold multiplicatively. Across seven backbones and five benchmarks (42 model--benchmark cells, three seeds each), CoRE improves the untrained base by +21.7 points on average versus +20.4 for majority-vote TTRL, wins wherever agreement is contestable with margins over the vote of up to +7.5 points, and reaches the voting baseline's plateau accuracy in 54--70% fewer steps. Consensus, not counting: treating the roll-out group as a graph rather than a ballot box turns a brittle vote into a calibrated, graded, self-supervised reward at no extra roll-out cost.