With the outstanding capabilities of Large Language Models (LLMs), solving math word problems (MWP) has greatly progressed, achieving higher performance on several benchmark datasets. However, it is more challenging to solve plane geometry problems (PGPs) due to the necessity of understanding, reasoning and computation on two modality data including both geometry diagrams and textual questions, where Multi-Modal Large Language Models (MLLMs) have not been extensively explored. Previous works simply regarded a plane geometry problem as multi-modal QA task, which ignored the importance of explicit parsing geometric elements from problems. To tackle this limitation, we propose to solve plane Geometry problems by Neural-Symbolic reasoning with MLLMs (GNS). We first leverage an MLLM to understand PGPs through knowledge prediction and symbolic parsing, next perform mathematical reasoning to obtain solutions, last adopt a symbolic solver to compute answers. Correspondingly, we introduce the largest PGPs dataset GNS-260K with multiple annotations including symbolic parsing, understanding, reasoning and computation. In experiments, our Phi3-Vision-based MLLM wins the first place on the PGPs solving task of MathVista benchmark, outperforming GPT-4o, Gemini Ultra and other much larger MLLMs. While LLaVA-13B-based MLLM markedly exceeded other close-source and open-source MLLMs on the MathVerse benchmark and also achieved the new SOTA on GeoQA dataset.

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, presenting a substantial risk of model overfitting and fails to accurately measure the genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly and readily applied across a diverse array of tasks. To this end, we introduce MathCheck, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MathCheck includes multiple mathematical reasoning tasks and robustness tests to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MathCheck, we develop MathCheck-GSM and MathCheck-GEO to assess mathematical textual reasoning and multi-modal reasoning capabilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MathCheck-GSM and MathCheck-GEO to evaluate over 26 LLMs and 17 multi-modal LLMs, assessing their comprehensive mathematical reasoning abilities. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MathCheck better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. Using MathCheck, we can also efficiently conduct informative behavior analysis to deeply investigate models. Finally, we show that our proposed checklist paradigm can easily extend to other reasoning tasks for their comprehensive evaluation.

Document dewarping aims to rectify deformations in photographic document images, thus improving text readability, which has attracted much attention and made great progress, but it is still challenging to preserve document structures. Given recent advances in diffusion models, it is natural for us to consider their potential applicability to document dewarping. However, it is far from straightforward to adopt diffusion models in document dewarping due to their unfaithful control on highly complex document images (e.g., 2000 × 3000 resolution). In this paper, we propose DvD, the first generative model to tackle document Dewarping via a Diffusion framework. To be specific, DvD introduces a coordinate-level denoising instead of typical pixel-level denoising, generating a mapping for deformation rectification. In addition, we further propose a time-variant condition refinement mechanism to enhance the preservation of document structures. In experiments, we find that current document dewarping benchmarks can not evaluate dewarping models comprehensively. To this end, we present AnyPhotoDoc6300, a rigorously designed large-scale document dewarping benchmark comprising 6,300 real image pairs across three distinct domains, enabling fine-grained evaluation of dewarping models. Comprehensive experiments demonstrate that our proposed DvD can achieve state-of-the-art performance with acceptable computational efficiency on multiple metrics across various benchmarks, including DocUNet, DIR300, and AnyPhotoDoc6300. The new benchmark and code will be publicly available at https://github.com/hanquansanren/DvD.

AI has made significant progress in solving math problems, but geometry problems remain challenging due to their reliance on both text and diagrams. In the text description, symbolic characters such as "ABC" often serve as a bridge to connect the corresponding diagram. However, by simply tokenizing symbolic characters into individual letters (e.g., 'A', 'B' and 'C'), existing works fail to study them explicitly and thus lose the semantic relationship with the diagram. In this paper, we develop a symbolic character-aware model to fully explore the role of these characters in both text and diagram understanding and optimize the model under a multi-modal reasoning framework. In the text encoder, we propose merging individual symbolic characters to form one semantic unit along with geometric information from the corresponding diagram. For the diagram encoder, we pre-train it under a multi-label classification framework with the symbolic characters as labels. In addition, we enhance the geometry diagram understanding ability via a self-supervised learning method under the masked image modeling auxiliary task. By integrating the proposed model into a general encoder-decoder pipeline for solving geometry problems, we demonstrate its superiority on two benchmark datasets, including GeoQA and Geometry3K, with extensive experiments. Specifically, on GeoQA, the question-solving accuracy is increased from 60.0% to 64.1%, achieving a new state-of-the-art accuracy; on Geometry3K, we reduce the question average solving steps from 6.9 down to 6.0 with marginally higher solving accuracy.