Related papers: GAPS: Geometry-Aware Problem Solver

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…

Understanding which concepts models can and cannot represent has been fundamental to many tasks: from effective and responsible use of models to detecting out of distribution data. We introduce Gaussian process probes (GPP), a unified and…

The encoding of input parameters is one of the fundamental building blocks of neural network algorithms. Its goal is to map the input data to a higher-dimensional space, typically supported by trained feature vectors. The mapping is crucial…

Accurate aerodynamic field prediction is crucial for vehicle drag evaluation, but the computational cost of high-fidelity CFD hinders its use in iterative design workflows. While learning-based methods enable fast and scalable inference,…

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…

In recent years, molecular representation learning has emerged as a key area of focus in various chemical tasks. However, many existing models fail to fully consider the geometric information of molecular structures, resulting in less…

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

This paper presents a comprehensive review of geometric constraint solving in parametric computer-aided design (CAD), with the major focus on its advances in the last 15 years. Geometric constraint solving can date back to the very first…

While 6D object pose estimation has recently made a huge leap forward, most methods can still only handle a single or a handful of different objects, which limits their applications. To circumvent this problem, category-level object pose…

Graph Neural Networks (GNNs) have become increasingly important due to their representational power and state-of-the-art predictive performance on many fundamental learning tasks. Despite this success, GNNs suffer from fairness issues that…

Geometric deep learning (GDL) has gained significant attention in scientific fields, for its proficiency in modeling data with intricate geometric structures. However, very few works have delved into its capability of tackling the…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

3D Gaussian Splatting has recently emerged as an efficient solution for high-quality and real-time novel view synthesis. However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured…

Rapid developments in advanced sensing and imaging have significantly enhanced information visibility, opening opportunities for predictive modeling of complex dynamic systems. However, sensing signals acquired from such complex systems are…

Outlier recognition is a fundamental problem in data analysis and has attracted a great deal of attention in the past decades. However, most existing methods still suffer from several issues such as high time and space complexities or…

With the emergence of Gaussian Splats, recent efforts have focused on large-scale scene geometric reconstruction. However, most of these efforts either concentrate on memory reduction or spatial space division, neglecting information in the…

Efficient identification of picking points is critical for automated fruit harvesting. Avocados present unique challenges owing to their irregular shape, weight, and less-structured growing environments, which require specific viewpoints…

We introduce ActiveGAMER, an active mapping system that utilizes 3D Gaussian Splatting (3DGS) to achieve high-quality, real-time scene mapping and exploration. Unlike traditional NeRF-based methods, which are computationally demanding and…

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…