Large Language Models (LLMs) have achieved remarkable success on reasoning benchmarks through Reinforcement Learning with Verifiable Rewards (RLVR), excelling at tasks such as math, coding, logic and puzzles. However, existing benchmarks evaluate only correctness, overlooking optimality—the ability to find the best solutions under constraints. We propose , the first comprehensive framework for training and evaluating LLMs on NP-hard optimization problems through quality-aware RLVR. provides three key components: a scalable training infrastructure with instance generators, quality verifiers, and optimal baselines across 10 tasks; a rigorous benchmark with 1,000 instances evaluating both feasibility (Success Rate) and quality (Quality Ratio); and quality-aware rewards enabling continuous improvement beyond binary correctness. Training on Qwen2.5-7B-Instruct-1M with 15K examples achieves 93.1% SR and 46.6% QR, significantly outperforming GPT-4o (29.6% SR, 14.6% QR). Beyond optimization, training on transfers to diverse tasks: mathematics (+2.2%), logic (+1.2%), knowledge (+4.1%), and instruction-following (+6.1%). Our analysis reveals quality-aware rewards improve solutions by 28.8% over binary rewards, and task diversity drives generalization more than data quantity—offering insights into RLVR scaling for complex reasoning.

Membership inference attacks (MIAs) aim to determine whether a specific example was used to train a given language model. While prior work has explored prompt-based attacks such as ReCALL, these methods rely heavily on the assumption that using known non-members as prompts reliably suppresses the model’s responses to non-member queries. We propose EM-MIA, a new membership inference approach that iteratively refines prefix effectiveness and membership scores using an expectation-maximization strategy without requiring labeled non-member examples. To support controlled evaluation, we introduce OLMoMIA, a benchmark that enables analysis of MIA robustness under systematically varied distributional overlap and difficulty. Experiments on WikiMIA and OLMoMIA show that EM-MIA outperforms existing baselines, particularly in settings with clear distributional separability. We highlight scenarios where EM-MIA succeeds in practical settings with partial distributional overlap, while failure cases expose fundamental limitations of current MIA methods under near-identical conditions. We release our code and evaluation pipeline to encourage reproducible and robust MIA research.

Quantifying uncertainty in black-box LLMs is vital for reliable responses and scalable oversight. Existing methods, which gauge a model’s uncertainty through evaluating self-consistency in responses to the target query, can be misleading: an LLM may confidently provide an incorrect answer to a target query, yet give a confident and accurate answer to that same target query when answering a knowledge-preserving perturbation of the query. We systematically analyze the model behaviors and demonstrate that this discrepancy stems from suboptimal retrieval of parametric knowledge, often due to contextual biases that prevent consistent access to stored knowledge. We then introduce DiverseAgentEntropy, a novel, theoretically-grounded method employing multi-agent interaction across diverse query variations for uncertainty estimation of black-box LLMs. This approach more accurately assesses an LLM’s true uncertainty and improves hallucination detection, outperforming existing self-consistency based techniques.