Teaching and Learning under Deductive Errors

2026-05-13

AI Summary

This work addresses a key limitation of classical machine teaching models, which assume learners perform deductive reasoning without error—contrary to the stochastic mistakes commonly observed in humans and large language models during few-shot learning. For the first time, we incorporate deductive errors into the Probably Approximately Correct (PAC) teaching framework, yielding a more realistic teaching–learning paradigm. We formulate six fundamental computational problems, establish a parameterized complexity analysis framework, and design XP algorithms parameterized by teaching set size. Leveraging standard complexity assumptions such as the Exponential Time Hypothesis (ETH), we derive tight runtime upper bounds. Empirical results demonstrate that the proposed protocol effectively captures and enhances the teachability of large language models.

Abstract

Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this does not hold. They fail on some consistency checks, and they can fail stochastically. In this paper we introduce a teaching and learning framework that takes these deductive errors into account. We specifically study the case of machine teaching, as different characterizations of the teacher can account for both machine teaching and learning. In an overhauled Probably Approximately Correct (PAC) setting, we study theoretically that, for some estimated error level, the teacher must find a PAC teaching set that with high probability will lead the learner to guess a hypothesis that is approximately correct. We study the computational complexity of six different problems related to computing optimal PAC teaching sets. We give XP algorithms parametrized by size of teaching set, with tight runtime bounds under standard complexity assumptions like ETH. These results are complemented with a small experimental study of which teaching and learning protocols can best represent the observed behavior in some LLM teaching sessions.

Problem

• deductive errors
• machine teaching
• PAC learning
• large language models
• computational complexity

Innovation

• deductive errors
• machine teaching
• PAC learning
• computational complexity
• few-shot learning