Trust Functions: Near Lossless Weak-to-Strong Generalization by Learning to Trust the Weak Teacher

Weak-to-strong generalization studies how to improve a strong student using supervision from a weaker teacher when reliable labels are scarce. We view this primarily as a data selection problem, where the key challenge is to identify which weak labels are reliable enough to serve as a training signal. To address this, we introduce trust functions that assign each weak label a scalar trust score and use these scores to filter weak supervision. Across several domains, including world knowledge, quantitative reasoning, decision making, trust filtering yields students that match and sometimes surpass ground-truth supervision, achieving near-lossless weak-to-strong generalization. Moreover, trust functions enable an iterative weak-to-strong chain that compounds gains by training a student and reusing it as the next teacher, producing the strongest final model. Our analyses suggest that neural trust functions improve learning through more than label error reduction. They induce an implicit easy-first curriculum, recover near-optimal alternatives where ground truth labels are incomplete, and produce more coherent gradient updates, offering a mechanistic account of the stability and efficiency of trust-filtered weak-to-strong generalization.

As AI systems become more capable, it becomes harder and more expensive for people to provide perfect answers for every task we want them to learn. This paper studies a practical alternative: using answers from a weaker AI system to train a stronger one, while avoiding the weaker system’s mistakes. Our main idea is to teach the stronger system when it should trust the weaker one. We introduce “trust functions,” which give each answer from the weaker system a score estimating how likely it is to be correct. Rather than training on all of the weaker system’s answers, we keep only the answers with high trust scores. These trust scores are learned from a small set of examples with known answers and then applied to new examples where the correct answers are not available. We test this approach on general knowledge questions, math problems, and chess puzzles. Across these settings, training on trusted answers from a weaker system often performs nearly as well as training on fully verified answers, and sometimes even performs better. We also show that this process can be repeated: each improved model can become the next teacher, leading to further gains. Overall, the paper shows that carefully choosing which weak answers to trust can make weak supervision much more useful for training stronger AI systems.