To adapt large language models (LLMs) to ranking tasks, existing list-wise methods, represented by list-wise Direct Preference Optimization (DPO), focus on optimizing partial-order or full-order list ranking consistency for LLMs to enhance their ranking abilities.However, we argue that optimizing top-K ranking consistency could be more appropriate for real-world applications. There are two main reasons: (1) users are typically concerned with only the top-K results, making top-K ranking more important, and (2) tail items often lack precise feedback, making top-K ranking more reliable. Based on this, we propose K-order Ranking Preference Optimization (KPO) by extending the DPO’s Plackett-Luce model to accommodate top-K rankings. Additionally, recognizing that the number of important items can vary across queries, we extend KPO to dynamically determine appropriate K for different samples and introduce a curriculum learning strategy to boost training efficiency. Extensive experiments demonstrate the effectiveness of KPO, highlighting its high sample efficiency and robustness to noise. The code is available at https://github.com/Lanyu0303/KPO.

Large language models have seen widespread adoption in math problem-solving, yet for geometry problems, which often necessitate visual aids even for humans, the most advanced multi-modal models still struggle to effectively utilize image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://anonymous.4open.science/r/GeoGPT4V-08B2.