Related papers: GAPS: Geometry-Aware Problem Solver
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…
Geometric programming (GP) is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a GP problem are deterministic and accurate.…
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…
Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive…
We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally,…
Mapping and localization are crucial problems in robotics and autonomous driving. Recent advances in 3D Gaussian Splatting (3DGS) have enabled precise 3D mapping and scene understanding by rendering photo-realistic images. However, existing…
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…
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…
Geometry mathematics problems pose significant challenges for large language models (LLMs) because they involve visual elements and spatial reasoning. Current methods primarily rely on symbolic character awareness to address these problems.…
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…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
Recent state-of-the-art methods for neural architecture search (NAS) exploit gradient-based optimization by relaxing the problem into continuous optimization over architectures and shared-weights, a noisy process that remains poorly…
Vision-Language Models (VLMs) often struggle with robust 3D spatial reasoning. Prevailing methods that rely on fine-tuning with 3D visual question-answering (VQA) datasets may overfit dataset-specific biases, while integrating specialized…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been…
This paper presents a new class of adaptive filters, namely Geometric-Algebra Adaptive Filters (GAAFs). They are generated by formulating the underlying minimization problem (a deterministic cost function) from the perspective of Geometric…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
Pre-trained 3D vision models have gained significant attention for their promising performance on point cloud data. However, fully fine-tuning these models for downstream tasks is computationally expensive and storage-intensive. Existing…
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…