Estimating problem difficulty without ground truth using Large Language Model comparisons

• URL: http://arxiv.org/abs/2512.14220v1
• Date: Tue, 16 Dec 2025 09:13:56 GMT
• Title: Estimating problem difficulty without ground truth using Large Language Model comparisons
• Authors: Marthe Ballon, Andres Algaba, Brecht Verbeken, Vincent Ginis,
• Abstract summary: We propose a new method for estimating problem difficulty, LLM compare.<n>An LLM performs pairwise difficulty comparisons, and then Bradley-Terry scores are computed based on the outcomes.<n>Our work represents a significant step towards replacing time-consuming human annotations and synthetic data generation.
• Score: 4.599673637363014
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recent advances in the finetuning of large language models (LLMs) have significantly improved their performance on established benchmarks, emphasizing the need for increasingly difficult, synthetic data. A key step in this data generation pipeline is a method for estimating problem difficulty. Current approaches, such as human calibration or performance-based scoring, fail to generalize to out-of-distribution problems, i.e. problems currently unsolvable by humans and LLMs, because they are not scalable, time-consuming, and ground truth dependent. Therefore, we propose a new method for estimating problem difficulty, LLM compare, that addresses these limitations. An LLM performs pairwise difficulty comparisons, and then Bradley-Terry scores are computed based on the outcomes. To validate our method, we first propose a conceptual framework that positions existing approaches on three orthogonal planes--construction, scale and dependence--identifying which quadrants a measure needs to occupy to score out-of-distribution problems. LLM compare naturally occupies all desirable quadrants as the first measure that is continuous and dynamic, model-agnostic and independent of ground truth information. As a second validation, we show that LLM compare demonstrates strong alignment with human annotations: Pearson $r \geq 0.80$ for $n=1876$. Thirdly, we show that LLM compare is robust to hallucinations, with less than $6\%$ degradation in Pearson correlation for $10\%$ noise injection. Our work represents a significant step towards replacing time-consuming human annotations and synthetic data generation, and will be an important driver for curriculum design, model evaluation, and AI-assisted research ideation.

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