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

arXiv: https://arxiv.org/abs/2608.09324 · HTML: https://mlsanity.com/paper/2608.09324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 41 of its 59 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 41)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)

## Abstract (arXiv)

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.