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Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…

This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

Vision transformers are effective deep learning models for vision tasks, including medical image segmentation. However, they lack efficiency and translational invariance, unlike convolutional neural networks (CNNs). To model long-range…

Reasoning about 3D objects based on 2D images is challenging due to variations in appearance caused by viewing the object from different orientations. Tasks such as object classification are invariant to 3D rotations and other such as pose…

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective…

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…

Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

Point cloud is a principal data structure adopted for 3D geometric information encoding. Unlike other conventional visual data, such as images and videos, these irregular points describe the complex shape features of 3D objects, which makes…

Deep convolutional neural networks (CNNs) have been intensively used for multi-class segmentation of data from different modalities and achieved state-of-the-art performances. However, a common problem when dealing with large, high…

Equivariant diffusion models have achieved impressive performance in 3D molecule generation. These models incorporate Euclidean symmetries of 3D molecules by utilizing an SE(3)-equivariant denoising network. However, specialized equivariant…

Analyzing a visual scene by inferring the configuration of a generative model is widely considered the most flexible and generalizable approach to scene understanding. Yet, one major problem is the computational challenge of the inference…

Deep Convolutional Neural Networks (CNNs) i.e. Residual Networks (ResNets) have been used successfully for many computer vision tasks, but are difficult to scale to 3D volumetric medical data. Memory is increasingly often the bottleneck…

This paper studies monocular visual odometry (VO) problem. Most of existing VO algorithms are developed under a standard pipeline including feature extraction, feature matching, motion estimation, local optimisation, etc. Although some of…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

This paper proposes a novel neural-network-based adaptive hybrid-reflectance three-dimensional (3-D) surface reconstruction model. The neural network combines the diffuse and specular components into a hybrid model. The proposed model…

Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance…

Deep neural networks have established themselves as the state-of-the-art methodology in almost all computer vision tasks to date. But their application to processing data lying on non-Euclidean domains is still a very active area of…