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Probing the Difficulty Perception Mechanism of Large Language Models
Created by
Haebom
Author
Sunbowen Lee, Qingyu Yin, Chak Tou Leong, Jialiang Zhang, Yicheng Gong, Shiwen Ni, Min Yang, Xiaoyu Shen
Outline
Although large-scale language models (LLMs) excel at problem-solving, research on their ability to internally assess problem difficulty is lacking. This study investigates whether LLMs implicitly encode problem difficulty in their internal representations. Using linear probes on the final token representation of LLMs, we demonstrate that they can linearly model the difficulty of mathematical problems. Furthermore, we discovered an opposite activation pattern for difficulty perception in a specific attention head of the final Transformer layer. This suggests that using LLMs as automatic difficulty annotators can reduce the reliance on costly human annotations required for benchmark building and training. We also found a significant difference between entropy and difficulty perception at the token level.
Takeaways, Limitations
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LLM can internally recognize the difficulty of a problem and model it linearly.
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A specific attention head in LLM plays an important role in difficulty perception.
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Leveraging LLM as an automatic difficulty annotator to suggest the possibility of building efficient benchmarks and developing educational courses.
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We found a correlation between entropy and perceived difficulty at the token level.
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The study focused on mathematical problems, so further research is needed to determine whether the results generalize to other types of problems.
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Further research is needed to fully understand the inner workings of the model.
