Related papers: FormalGeo: An Extensible Formalized Framework for …
We study visual explanation in geometry education as a Referring Image Segmentation (RIS) problem: given a diagram and a natural language description, the task is to produce a pixel-level mask for the referred geometric element. However,…
Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics…
As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based…
Efficient and accurate autoformalization methods, which leverage large-scale datasets of extensive natural language mathematical problems to construct formal language datasets, are key to advancing formal mathematical reasoning. In this…
Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space,…
We present AlphaGeometry2 (AG2), a significantly improved version of AlphaGeometry introduced in (Trinh et al., 2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend…
Geometric problem solving has always been a long-standing challenge in the fields of mathematical reasoning and artificial intelligence. We built a neural-symbolic system, called FGeo-HyperGNet, to automatically perform human-like geometric…
Large Language Models (LLMs), such as ChatGPT, demonstrate a strong understanding of human natural language and have been explored and applied in various fields, including reasoning, creative writing, code generation, translation, and…
Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains…
As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier.…
Wireless localization of permanent magnets enables occlusion-free guidance for medical interventions, yet its practical accuracy is fundamentally limited by two coupled challenges: the poor observability of conventional planar sensor arrays…
Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic…
Geometric reasoning remains a core challenge for Multimodal Large Language Models (MLLMs). Even the most advanced closed-source systems, such as GPT-O3 and Gemini-2.5-Pro, still struggle to solve geometry problems reliably, despite…
Applying AI foundation models directly to geospatial datasets remains challenging due to their limited ability to represent and reason with geographical entities, specifically vector-based geometries and natural language descriptions of…
Geometry problem solving (GPS) requires capacities of multi-modal understanding, multi-hop reasoning and theorem knowledge application. In this paper, we propose a neural-symbolic model for plane geometry problem solving (PGPS), named…
Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable…
Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal…
With the rapid advancement of large language models, there has been a growing interest in their capabilities in mathematical reasoning. However, existing research has primarily focused on text-based algebra problems, neglecting the study of…
Autoformalization, which translates natural language mathematics into formal statements to enable machine reasoning, faces fundamental challenges in the wild due to the multimodal nature of the physical world, where physics requires…
Formal mathematics is the discipline of translating mathematics into a programming language in which any statement can be unequivocally checked by a computer. Mathematicians and computer scientists have spent decades of painstaking…