Related papers: Grounding Continuous Representations in Geometry: …

This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…

Neural Radiance Fields (NeRF) have shown remarkable success in image novel view synthesis (NVS), inspiring extensions to LiDAR NVS. However, most methods heavily rely on accurate camera poses for scene reconstruction. The sparsity and…

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…

Point cloud segmentation is the foundation of 3D environmental perception for modern intelligent systems. To solve this problem and image segmentation, conditional random fields (CRFs) are usually formulated as discrete models in label…

Neural surrogates enable orders-of-magnitude acceleration of computational fluid dynamics (CFD) simulations, with the potential to transform engineering and healthcare workflows. Neural surrogate use in real-world applications requires…

Graph Neural Networks (GNNs) are key tools for graph representation learning, demonstrating strong results across diverse prediction tasks. In this paper, we present Convexified Message-Passing Graph Neural Networks (CGNNs), a novel and…

Neural radiance fields (NeRFs) are a powerful tool for implicit scene representations, allowing for differentiable rendering and the ability to make predictions about unseen viewpoints. There has been growing interest in object and…

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…

In this paper we construct and theoretically analyse group equivariant convolutional kernel networks (CKNs) which are useful in understanding the geometry of (equivariant) CNNs through the lens of reproducing kernel Hilbert spaces (RKHSs).…

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned…

The recent advance of neural fields, such as neural radiance fields, has significantly pushed the boundary of scene representation learning. Aiming to boost the computation efficiency and rendering quality of 3D scenes, a popular line of…

It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…

Neural network representation learning for spatial data is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and…

Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied…

Neural Radiance Fields (NeRF) achieves photo-realistic image rendering from novel views, and the Neural Scene Graphs (NSG) \cite{ost2021neural} extends it to dynamic scenes (video) with multiple objects. Nevertheless, computationally heavy…