Related papers: GOLD: Geometry Problem Solver with Natural Languag…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…

We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary…

Geologic map, as a fundamental diagram in geology science, provides critical insights into the structure and composition of Earth's subsurface and surface. These maps are indispensable in various fields, including disaster detection,…

Automatically generating maps from satellite images is an important task. There is a body of literature which tries to address this challenge. We created a more expansive survey of the task by experimenting with different models and adding…

The ability to accomplish tasks via natural language instructions is one of the most efficient forms of interaction between humans and technology. This efficiency has been translated into practical applications with generative AI tools now…

Large language models (LLMs) have been enormously successful in solving a wide variety of structured and unstructured generative tasks, but they struggle to generate procedural geometry in Computer Aided Design (CAD). These difficulties…

Artificial intelligence (AI) can accelerate the design of materials by identifying correlations and complex patterns in data. However, AI methods commonly attempt to describe the entire, immense materials space with a single model, while it…

This paper introduces a new metamodel-based knowledge representation that significantly improves autonomous learning and adaptation. While interest in hybrid machine learning / symbolic AI systems leveraging, for example, reasoning and…

This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…

Geometric understanding - including depth and height perception - is fundamental to intelligence and crucial for navigating our environment. Despite the impressive capabilities of large Vision Language Models (VLMs), it remains unclear how…

We demonstrate how language can improve geolocation: the task of predicting the location where an image was taken. Here we study explicit knowledge from human-written guidebooks that describe the salient and class-discriminative visual…

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…

Large language models (LLMs) struggle with formal domains that require rigorous logical deduction and symbolic reasoning, such as mathematical proof generation. We propose a neuro-symbolic approach that combines LLMs' generative strengths…

Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…

We investigate transductive zero-shot point cloud semantic segmentation, where the network is trained on seen objects and able to segment unseen objects. The 3D geometric elements are essential cues to imply a novel 3D object type. However,…

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,…