GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language

Multi-modal Large Language Models (MLLMs) have gained significant attention in both academia and industry for their capabilities in handling multi-modal tasks. However, these models face challenges in mathematical geometric reasoning due to the scarcity of high-quality geometric data. To address this issue, synthetic geometric data has become an essential strategy. Current methods for generating synthetic geometric data involve rephrasing or expanding existing problems and utilizing predefined rules and templates to create geometric images and problems. However, these approaches often produce data that lacks diversity or is prone to noise. Additionally, the geometric images synthesized by existing methods tend to exhibit limited variation and deviate significantly from authentic geometric diagrams. To overcome these limitations, we propose GeoFM, a novel method for synthesizing geometric data. GeoFM uses formal languages to explore combinations of conditions within metric space, generating high-fidelity geometric problems that differ from the originals while ensuring correctness through a symbolic engine. Experimental results show that our synthetic data significantly outperforms existing methods. The model trained with our data surpass the proprietary GPT-4o model by 18.7\% on geometry problem-solving tasks in MathVista and by 16.5\% on GeoQA. Additionally, it exceeds the performance of a leading open-source model by 5.7\% on MathVista and by 2.7\% on GeoQA.

Improving Factual Error Correction for Abstractive Summarization via Data Distillation and Conditional-generation Cloze

Improving factual consistency in abstractive summarization has been a focus of current research. One promising approach is the post-editing method. However, previous works have yet to make sufficient use of factual factors in summaries and suffers from the negative effect of the training datasets. In this paper, we first propose a novel factual error correction model FactCloze based on a conditional-generation cloze task. FactCloze can construct the causality among factual factors while being able to determine whether the blank can be answered or not. Then, we propose a data distillation method to generate a more faithful summarization dataset SummDSC via multiple-dimensional evaluation. We experimentally validate the effectiveness of our approach, which leads to an improvement in multiple factual consistency metrics compared to baselines.

Just ClozE! A Fast and Simple Method for Evaluating the Factual Consistency in Abstractive Summarization

The issue of factual consistency in abstractive summarization has attracted much attention in recent years, and the evaluation of factual consistency between summary and document has become an important and urgent task. Most of the current evaluation metrics are adopted from the question answering (QA). However, the application of QA-based metrics is extremely time-consuming in practice, causing the iteration cycle of abstractive summarization research to be severely prolonged. In this paper, we propose a new method called ClozE to evaluate factual consistency by cloze model, instantiated based on masked language model(MLM), with strong interpretability and substantially higher speed. We demonstrate that ClozE can reduce the evaluation time by nearly 96$\%$ relative to QA-based metrics while retaining their interpretability and performance through experiments on six human-annotated datasets and a meta-evaluation benchmark GO FIGURE \citep{gabriel2020go}. We also implement experiments to further demonstrate more characteristics of ClozE in terms of performance and speed. In addition, we conduct an experimental analysis of the limitations of ClozE, which suggests future research directions. The code and models for ClozE will be released upon the paper acceptance.