Ask-E: An Environment for Calibrated Question Generation

Abstract

Today, we improve models by training and evaluating them on problems at the frontier of their abilities. Creating such problems is itself a demanding task, requiring the ability to probe model limits and generalize beyond existing question distributions. It also means placing problems at a precise difficulty level, which requires understanding what it takes to solve them. In short, generating problems calibrated to a model's current frontier demands capability beyond it, an increasingly burdensome constraint as models improve. Our key insight is that we can leverage this constraint to our advantage: a model that can generate problems consistently calibrated to a given frontier must possess capability beyond it. Accordingly, we present Ask-E, an environment that benchmarks and trains models on their ability to write questions at a given skill level, rather than answer them. Concretely, we define target skill levels as ranges bounded by the capabilities of two existing language models. A generated question is successfully calibrated if exactly one of the two models can solve it, placing it precisely within the target range and differentiating the capabilities of these models. Ask-E serves both as a benchmark and a training environment, where models generate problems calibrated to a variety of skill levels. We find that even frontier models achieve below 50% calibration on the benchmark, leaving significant headroom to measure future progress. We also show that training on this environment leads to improvements across a number of downstream math benchmarks even with no new math data, no interaction with stronger models, and no correctness-based reward.