Related papers: Grounding Continuous Representations in Geometry: …

Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Normal estimation for unstructured point clouds is an important task in 3D computer vision. Current methods achieve encouraging results by mapping local patches to normal vectors or learning local surface fitting using neural networks.…

Phase-field (PF) simulation provides a powerful framework for predicting microstructural evolution but suffers from prohibitive computational costs that severely limit accessible spatiotemporal scales in practical applications. While…

Machine learning (ML) has been increasingly applied in concrete research to optimize performance and mixture design. However, one major challenge in applying ML to cementitious materials is the limited size and diversity of available…

Neural Radiance Fields (NeRF) have demonstrated impressive performance in novel view synthesis. However, NeRF and most of its variants still rely on traditional complex pipelines to provide extrinsic and intrinsic camera parameters, such as…

Equivariant neural networks (ENNs) are graph neural networks embedded in $\mathbb{R}^3$ and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on…

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no…

Neural material representations are becoming a popular way to represent materials for rendering. They are more expressive than analytic models and occupy less memory than tabulated BTFs. However, existing neural materials are immutable,…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled…

Neural Radiance Fields (NeRF) achieve photo-realistic view synthesis with densely captured input images. However, the geometry of NeRF is extremely under-constrained given sparse views, resulting in significant degradation of novel view…

Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the…

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…

This paper introduces CoFie, a novel local geometry-aware neural surface representation. CoFie is motivated by the theoretical analysis of local SDFs with quadratic approximation. We find that local shapes are highly compressive in an…

Despite significant progress of deep learning in recent years, state-of-the-art semantic matching methods still rely on legacy features such as SIFT or HoG. We argue that the strong invariance properties that are key to the success of…

Neural Processes (NPs) are meta-learning models that learn to map sets of observations to approximations of the corresponding posterior predictive distributions. By accommodating variable-sized, unstructured collections of observations and…

Neural encoding models aim to predict fMRI-measured brain responses to natural images. fMRI data is acquired as a 3D volume of voxels, where each voxel has a defined spatial location in the brain. However, conventional encoding models often…