Sunbowen Lee

Chak Tou Leong, Dingwei Chen, Heming Xia et al.

Large reasoning models (LRMs) have achieved remarkable success in complex problem-solving, yet they often suffer from computational redundancy or reasoning unfaithfulness. Current methods for shaping LRM behavior typically rely on reinforcement learning or fine-tuning with gold-standard reasoning traces, a paradigm that is both computationally expensive and difficult to scale. In this paper, we reveal that LRMs possess latent \textit{reasoning beliefs} that internally track their own reasoning traits, which can be captured through simple logit probing. Building upon this insight, we propose Reasoning Belief Engineering (RELIEF), a simple yet effective framework that shapes LRM behavior by aligning the model's self-concept with a target belief blueprint. Crucially, RELIEF completely bypasses the need for reasoning-trace supervision. It internalizes desired traits by fine-tuning on synthesized, self-reflective question-answering pairs that affirm the target belief. Extensive experiments on efficiency and faithfulness tasks demonstrate that RELIEF matches or outperforms behavior-supervised and preference-based baselines while requiring lower training costs. Further analysis validates that shifting a model's reasoning belief effectively shapes its actual behavior.

Sunbowen Lee, Qingyu Yin, Chak Tou Leong et al.

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.