LLM judges are increasingly used to evaluate open-ended responses, but their scores depend strongly on the rubrics that condition them. A vague rubric asking for a response to be “helpful and factual” can reward polished answers that invent facts or violate user intent. We treat reusable rubrics as measurement specifications: changing the rubric changes the response quality measurement induced by a fixed judge. We introduce PReMISE, a framework that, given pairwise human-preference data, (i) discovers a policy-level rubric set, and (ii) audits any rubric set under LLM-judge use along four axes: structural adequacy, reliability, preference fit, and adversarial robustness. We evaluate PReMISE on four public human-preference corpora – UltraFeedback, Arena-Expert-5K, HelpSteer3, and HH-RLHF – across six rubric sources and three open-weight judges spanning 32B to 1T parameters. Across rubric sources no raw source is simultaneously reliable, preference-predictive, and adversarially robust; and high inter-rater agreement does not imply low exploitability. PReMISE is the only rubric source to score non-trivially on applicability, specificity, and effective dimensionality simultaneously. We contribute two audit-targeted repair operations: preference-rank selection raises held-out cross-source, cross-judge mean accuracy on paired responses from 65.0% to 68.6%, competitive with the strongest rubric-discovery baselines and leading on two of three judges in our cross-judge sweep; reliability-constrained refinement reduces the rate at which exploit responses receive high scores from 46.4% to 36.0% with little change in inter-judge agreement (𝛼=.531→.519).

Training process reward models (PRMs) requires step-level correctness labels, obtained either through expensive human annotation or by relying on ground-truth answers, limiting the ability to scale process-level supervision. We propose ScalePRM, which scales verification compute as an alternative: given a problem and a candidate solution, we generate multiple independent verifications of each reasoning step and aggregate their judgments to produce synthetic step-level labels without ground truth. We explore two representative inference-time scaling strategies, parallel scaling through self-consistency and sequential scaling through meta-critique, and train generative PRMs on the resulting synthetic data. On ProcessBench, a benchmark for identifying erroneous steps in mathematical reasoning, PRMs trained on step-level self-consistency data achieve 67.5 F1, surpassing reference-guided training with ground-truth access (66.4 F1) and GPT-4o as a critic (61.9 F1). When deployed as reward signals in RL training with Qwen2.5-Math-7B, our best PRM achieves 47.4% average accuracy across six mathematical reasoning benchmarks, outperforming ground-truth-based RLVR (43.9%). We also identify and address reward exploitation patterns unique to generative PRM-based RL. Our results demonstrate that scaling verification compute is a viable alternative to ground-truth supervision for training process reward models.

Large Language Models (LLMs) have shown remarkable reasoning capabilities in mathematical and scientific tasks. To enhance complex reasoning, multi-agent systems have been proposed to harness the collective intelligence of LLM agents. However, existing collaboration structures are either predefined or rely on majority voting or round-table debates, which can suppress correct but less dominant agent contributions. Recent approaches model multi-agent systems as graph networks but optimize purely for agent performance, neglecting the quality of interactions. We hypothesize that effective agent communication is crucial for multi-agent reasoning and that debating quality plays a significant role. To address this, we propose OptAgent, a multi-agent verbal reinforcement learning algorithm that dynamically constructs and refines multi-agent collaboration structures. Our method defines action spaces and a feedback mechanism that evaluates communication robustness and coherence throughout the debate. The final decision is achieved through a majority vote over all the agents. We assess OptAgent on various reasoning tasks, including mathematical reasoning, creative writing, scientific reasoning, and numerical sorting. Results demonstrate that our approach significantly outperforms single-agent prompting methods and state-of-the-art multi-agent frameworks on diverse tasks.