相关论文: Embed Me If You Can: A Geometric Perceptron

Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…

The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…

Invariant object recognition is one of the most fundamental cognitive tasks performed by the brain. In the neural state space, different objects with stimulus variabilities are represented as different manifolds. In this geometrical…

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired…

Aiming at drastic speedup for point-feature embeddings at test time, we propose a new framework that uses a pair of multi-layer perceptrons (MLP) and a lookup table (LUT) to transform point-coordinate inputs into high-dimensional features.…

Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…

Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learning (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models are often complicated and hardly interpretable, which poses…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

4D modeling of human-object interactions is critical for numerous applications. However, efficient volumetric capture and rendering of complex interaction scenarios, especially from sparse inputs, remain challenging. In this paper, we…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

In this paper, we described and developed a framework for Multilayer Perceptron (MLP) to work on low level image processing, where MLP will be used to perform image super-resolution. Meanwhile, MLP are trained with different types of images…

Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way. For networks, previously proposed systems are developed. Perceptron networks in disjunctive…

A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very…

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…

This work provides an architecture that incorporates depth and tactile information to create rich and accurate 3D models useful for robotic manipulation tasks. This is accomplished through the use of a 3D convolutional neural network (CNN).…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

Multi-modal Large Language Models (MLLMs) have advanced greatly in general tasks. However, they still face challenges in geometric reasoning, a task that requires synergistic integration of visual recognition proficiency and complex…

Models for image representation learning are typically designed for either recognition or generation. Various forms of contrastive learning help models learn to convert images to embeddings that are useful for classification, detection, and…

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…

We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Previous methods focus on learning point weights to fit neighborhoods into a geometric…