Question Difficulty Estimation for Large Language Models via Answer Plausibility Scoring

Problem
This paper addresses the gap in effective question difficulty estimation for large language models (LLMs) in question answering (QA) systems. Existing methodologies primarily rely on readability metrics, retrieval-based signals, or popularity statistics, which inadequately capture the nuanced reasoning challenges that LLMs face. The authors propose a novel approach, Q-DAPS (Question Difficulty based on Answer Plausibility Scores), to fill this gap. This work is presented as a preprint and has not yet undergone peer review.

Method
Q-DAPS estimates question difficulty by calculating the entropy of plausibility scores derived from candidate answers. The method involves generating multiple plausible answers for a given question and assessing their plausibility using a scoring mechanism. The entropy of these scores serves as a measure of difficulty, with higher entropy indicating greater uncertainty and thus higher difficulty. The authors evaluate Q-DAPS across four prominent QA datasets: TriviaQA, Natural Questions (NQ), MuSiQue, and QASC. The architecture specifics, loss functions, and training compute are not disclosed, but the method is designed to be interpretable and scalable, with robustness across various hyperparameter settings and question types.

Results
Q-DAPS consistently outperforms baseline methods across all evaluated datasets. The authors report significant improvements in correlation with human judgments of question difficulty, with specific effect sizes not disclosed in the abstract. The robustness of Q-DAPS is further validated through extensive ablation studies, demonstrating its effectiveness across different plausibility estimation paradigms and model sizes. The paper indicates that Q-DAPS maintains performance stability even under varying conditions, suggesting its practical applicability in real-world QA systems.

Limitations
The authors acknowledge that while Q-DAPS shows strong performance, it may still be sensitive to the quality of the underlying language model used for generating plausible answers. Additionally, the reliance on entropy as a measure may not capture all dimensions of question difficulty, particularly in highly specialized domains. The paper does not address potential biases in the training data that could affect the plausibility scoring mechanism, nor does it explore the computational overhead associated with generating multiple plausible answers.

Why it matters
The introduction of Q-DAPS has significant implications for the development of more effective QA systems. By providing a robust and interpretable method for estimating question difficulty, this work enhances the ability of LLMs to tackle complex reasoning tasks. Improved difficulty estimation can lead to better model training strategies, more effective question selection for evaluation, and ultimately, advancements in the performance of LLMs in real-world applications. This research paves the way for future studies to explore the integration of difficulty estimation into adaptive learning systems and personalized education tools.

Authors: Jamshid Mozafari, Bhawna Piryani, Adam Jatowt
Source: arXiv:2605.12398
URL: https://arxiv.org/abs/2605.12398v1