AdaptMI: Adaptive Skill-based In-context Math Instructions for Small Language Models

In-context learning (ICL) enhances language model performance by providing relevant contextual information.Recent works (Didolkar et al., 2024a;b) show that ICL performance can be improved by leveraging a frontier largelanguage model’s (LLM) ability to predict required skills to solve a problem, popularly referred to as an LLM’smetacognition, and using the recommended skills to construct necessary in-context examples. While this improvesperformance in larger models, smaller language models (SLMs) see minimal benefit, revealing a performance gap.We show that skill-based prompting can hurt SLM performance on easy questions by introducing unnecessaryinformation, akin to cognitive overload. To mitigate this, we introduce AdaptMI, an Adaptive strategy forselecting skill-based Math Instructions. Guided by cognitive load theory, AdaptMI introduces skill-basedexamples only when the model performs poorly. We further propose AdaptMI+ , which provides targetedexamples for specific missing skills. In 5-shot evaluations on popular math benchmarks and five SLMs (1B–7B;Qwen, Llama), AdaptMI+ improves accuracy by up to 6% compared to naive skill-based methods.