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We introduce clever, the first curated benchmark for evaluating the generation of specifications and formally verified code in lean 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. 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 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 Back in the early 20th century, a horse named hans appeared to perform arithmetic and other intellectual tasks during exhibitions in germany, while it actually relied solely on involuntary cues in.

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