AdaptMI: Adaptive Skill-based In-context Math Instruction for Small Language Models
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912581043617792 |
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| author | He, Yinghui Panigrahi, Abhishek Lin, Yong Arora, Sanjeev |
| author_facet | He, Yinghui Panigrahi, Abhishek Lin, Yong Arora, Sanjeev |
| contents | In-context learning (ICL) allows a language model to improve its problem-solving capability when provided with suitable information in context. Since the choice of in-context information can be determined based on the problem itself, in-context learning is analogous to human learning from teachers in a classroom. Recent works (Didolkar et al., 2024a; 2024b) show that ICL performance can be improved by leveraging a frontier large language model's (LLM) ability to predict required skills to solve a problem, popularly referred to as an LLM's metacognition, and using the recommended skills to construct necessary in-context examples. While this skill-based strategy boosts ICL performance in larger models, its gains on small language models (SLMs) have been minimal, highlighting a performance gap in ICL capabilities. We investigate this gap and show that skill-based prompting can hurt SLM performance on easy questions by introducing unnecessary information, akin to cognitive overload. To address this, we introduce AdaptMI, an adaptive approach to selecting skill-based in-context Math Instructions for SLMs. Inspired by cognitive load theory from human pedagogy, our method only introduces skill-based examples when the model performs poorly. We further propose AdaptMI+, which adds examples targeted to the specific skills missing from the model's responses. On 5-shot evaluations across popular math benchmarks and five SLMs (1B--7B; Qwen, Llama), AdaptMI+ improves accuracy by up to 6% over naive skill-based strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | AdaptMI: Adaptive Skill-based In-context Math Instruction for Small Language Models He, Yinghui Panigrahi, Abhishek Lin, Yong Arora, Sanjeev Computation and Language In-context learning (ICL) allows a language model to improve its problem-solving capability when provided with suitable information in context. Since the choice of in-context information can be determined based on the problem itself, in-context learning is analogous to human learning from teachers in a classroom. Recent works (Didolkar et al., 2024a; 2024b) show that ICL performance can be improved by leveraging a frontier large language model's (LLM) ability to predict required skills to solve a problem, popularly referred to as an LLM's metacognition, and using the recommended skills to construct necessary in-context examples. While this skill-based strategy boosts ICL performance in larger models, its gains on small language models (SLMs) have been minimal, highlighting a performance gap in ICL capabilities. We investigate this gap and show that skill-based prompting can hurt SLM performance on easy questions by introducing unnecessary information, akin to cognitive overload. To address this, we introduce AdaptMI, an adaptive approach to selecting skill-based in-context Math Instructions for SLMs. Inspired by cognitive load theory from human pedagogy, our method only introduces skill-based examples when the model performs poorly. We further propose AdaptMI+, which adds examples targeted to the specific skills missing from the model's responses. On 5-shot evaluations across popular math benchmarks and five SLMs (1B--7B; Qwen, Llama), AdaptMI+ improves accuracy by up to 6% over naive skill-based strategies. |
| title | AdaptMI: Adaptive Skill-based In-context Math Instruction for Small Language Models |
| topic | Computation and Language |
| url | https://arxiv.org/abs/2505.00147 |