相关论文: Gold-medalist Performance in Solving Olympiad Geom…
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…
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.…
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…
World models serve as essential building blocks toward Artificial General Intelligence (AGI), enabling intelligent agents to predict future states and plan actions by simulating complex physical interactions. However, existing interactive…
This paper presents a new algorithm for filling holes in Level of Detail 2 (LoD2) building mesh models, addressing the challenges posed by geometric inaccuracies and topological errors. Unlike traditional methods that often alter the…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
The availability of low cost sensors has led to an unprecedented growth in the volume of spatial data. However, the time required to evaluate even simple spatial queries over large data sets greatly hampers our ability to interactively…
Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning…
In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
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…
The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…
Geometry problem solving has garnered increasing attention due to its potential applications in intelligent education field. Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents…
We introduce the Granite Embedding R2 models, a comprehensive family of high-performance English encoder-based embedding models engineered for enterprise-scale dense retrieval applications. Building upon our first-generation release, these…
Physics provides fundamental laws that describe and predict the natural world. AI systems aspiring toward more general, real-world intelligence must therefore demonstrate strong physics problem-solving abilities: to formulate and apply…
Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality,…
Spatial intelligence is a critical frontier for Multimodal Large Language Models (MLLMs), empowering them to comprehend the physical world. Drawing inspiration from human perception mechanisms, prior studies attempt to construct a spatial…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
LLMs have made significant progress in complex but easy-to-verify problems, yet they still struggle with discovering the unknown. In this paper, we present \textbf{AlphaResearch}, an autonomous research agent designed to discover new…
Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are…