Probing the Difficulty Perception Mechanism of Large Language Models

Fuente: arXiv
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Main Authors: Lee, Sunbowen, Yin, Qingyu, Leong, Chak Tou, Zhang, Jialiang, Gong, Yicheng, Ni, Shiwen, Yang, Min, Shen, Xiaoyu
Format: Preprint
Published: 2025
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_version_ 1866911205542592512
author Lee, Sunbowen
Yin, Qingyu
Leong, Chak Tou
Zhang, Jialiang
Gong, Yicheng
Ni, Shiwen
Yang, Min
Shen, Xiaoyu
author_facet Lee, Sunbowen
Yin, Qingyu
Leong, Chak Tou
Zhang, Jialiang
Gong, Yicheng
Ni, Shiwen
Yang, Min
Shen, Xiaoyu
contents Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient resource allocation. In this work, we investigate whether LLMs implicitly encode problem difficulty in their internal representations. Using a linear probe on the final-token representations of LLMs, we demonstrate that the difficulty level of math problems can be linearly modeled. We further locate the specific attention heads of the final Transformer layer: these attention heads have opposite activation patterns for simple and difficult problems, thus achieving perception of difficulty. Our ablation experiments prove the accuracy of the location. Crucially, our experiments provide practical support for using LLMs as automatic difficulty annotators, potentially substantially reducing reliance on costly human labeling in benchmark construction and curriculum learning. We also uncover that there is a significant difference in entropy and difficulty perception at the token level. Our study reveals that difficulty perception in LLMs is not only present but also structurally organized, offering new theoretical insights and practical directions for future research. Our code is available at https://github.com/Aegis1863/Difficulty-Perception-of-LLMs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_05969
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Probing the Difficulty Perception Mechanism of Large Language Models
Lee, Sunbowen
Yin, Qingyu
Leong, Chak Tou
Zhang, Jialiang
Gong, Yicheng
Ni, Shiwen
Yang, Min
Shen, Xiaoyu
Computation and Language
Artificial Intelligence
Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient resource allocation. In this work, we investigate whether LLMs implicitly encode problem difficulty in their internal representations. Using a linear probe on the final-token representations of LLMs, we demonstrate that the difficulty level of math problems can be linearly modeled. We further locate the specific attention heads of the final Transformer layer: these attention heads have opposite activation patterns for simple and difficult problems, thus achieving perception of difficulty. Our ablation experiments prove the accuracy of the location. Crucially, our experiments provide practical support for using LLMs as automatic difficulty annotators, potentially substantially reducing reliance on costly human labeling in benchmark construction and curriculum learning. We also uncover that there is a significant difference in entropy and difficulty perception at the token level. Our study reveals that difficulty perception in LLMs is not only present but also structurally organized, offering new theoretical insights and practical directions for future research. Our code is available at https://github.com/Aegis1863/Difficulty-Perception-of-LLMs.
title Probing the Difficulty Perception Mechanism of Large Language Models
topic Computation and Language
Artificial Intelligence
url https://arxiv.org/abs/2510.05969