Related papers: Towards Generating Controllable and Solvable Geome…
This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…
Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories:…
Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either…
Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to…
The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB). Central to our method is a new domain-specific…
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…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
Mathematical problem generation (MPG) is a significant research direction in the field of intelligent education. In recent years, the rapid development of large language models (LLMs) has enabled new technological approaches to…
Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial…
The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This…
Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges…
We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks. Existing data generation approaches rely on open-loop pipelines and…
Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric…
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)…
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…
Scene understanding is a critical problem in computer vision. In this paper, we propose a 3D point-based scene graph generation ($\mathbf{SGG_{point}}$) framework to effectively bridge perception and reasoning to achieve scene understanding…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…