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Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two…
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…
AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the…
Large Language Models (LLMs) present massive inherent knowledge and superior semantic comprehension capability, which have revolutionized various tasks in natural language processing. Despite their success, a critical gap remains in…
The digitization of traffic sensing infrastructure has significantly accumulated an extensive traffic data warehouse, which presents unprecedented challenges for transportation analytics. The complexities associated with querying…
Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS)…
Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…
Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This…
Current GP frameworks are highly effective on a range of real and simulated benchmarks. However, due to the high dimensionality of the genotypes for GP, the task of visualising the fitness landscape for GP search can be difficult. This…
This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of…
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…
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
Recent progress in large language models has made them increasingly capable research assistants in mathematics. Yet, as their reasoning abilities improve, evaluating their mathematical competence becomes increasingly challenging. The…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved…
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,…
Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge,…