Mayur Naik

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to \~10\% behind frontier models in accuracy but they are up to \~25\% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1\% in accuracy and 15.9\% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We will make the benchmark open by releasing the evaluation pipeline, generated problems, and a public leaderboard that updates as new models are released.

To identify safety violations, auditors often search over large sets of agent traces. This search is difficult because failures are often rare, complex, and sometimes even adversarially hidden and only detectable when multiple traces are analyzed together. These challenges arise in diverse settings such as misuse campaigns, covert sabotage, and reward hacking. Existing approaches struggle here for a couple of reasons. Per-trace monitors miss failures that only become visible across traces and naive agentic auditing does not scale to large trace collections. We introduce Meerkat, which combines clustering with agentic search to uncover violations specified in natural language. Through structured search and adaptive investigation of promising regions, Meerkat finds sparse failures without relying on seed scenarios, fixed workflows, or exhaustive enumeration. Across misuse, misalignment, and task gaming settings, Meerkat significantly improves detection of safety violations over baseline monitors, discovers widespread developer cheating on a top agent benchmark, and finds nearly 4x more examples of reward hacking on CyBench than previous audits.