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We introduce clever, the first curated benchmark for evaluating the generation of specifications and formally verified code in lean Our method, stair (safety alignment with introspective reasoning), guides models to think more carefully before responding. The benchmark comprises of 161 programming problems

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Our analysis yields a novel robustness metric called clever, which is short for cross lipschitz extreme value for network robustness One common approach is training models to refuse unsafe queries, but this strategy can be vulnerable to clever prompts, often referred to as jailbreak attacks, which can trick the ai into providing harmful responses Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers

To measure this ability in machine learning models, we introduce math, a new dataset of 12,500 challenging competition mathematics problems

With a clever usage of the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines (i) a preference optimization loss that directly aligns the policy with human preference, and (ii) a supervised learning loss which explicitly imitates the policy with a baseline distribution. Across evaluated tasks, rahp yields compact models with stronger clever lower bounds and minimal change in clean accuracy, and it improves resistance to a wide variety of strong attacks