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The challenge of image generation has been effectively modeled as a problem of structure priors or transformation. However, existing models have unsatisfactory performance in understanding the global input image structures because of…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…
Suffering from the multi-view data diversity and complexity for semi-supervised classification, most of existing graph convolutional networks focus on the networks architecture construction or the salient graph structure preservation, and…
Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized…
In recent years, with the rapid development of computer information technology, the development of artificial intelligence has been accelerating. The traditional geometry recognition technology is relatively backward and the recognition…
Handling geometric transformations, particularly rotations, remains a challenge in deep learning for computer vision. Standard neural networks lack inherent rotation invariance and typically rely on data augmentation or architectural…
Recently, FCNs have attracted widespread attention in the CD field. In pursuit of better CD performance, it has become a tendency to design deeper and more complicated FCNs, which inevitably brings about huge numbers of parameters and an…
Rotation-equivariance is an essential yet challenging property in oriented object detection. While general object detectors naturally leverage robustness to spatial shifts due to the translation-equivariance of the conventional CNNs,…
Reconstructing coherent 3D geometry and appearance from unposed multi-view images is a fundamental yet challenging problem in computer vision. Most existing visual geometry foundation models predict explicit geometry by regressing…
By recursively summing node features over entire neighborhoods, spatial graph convolution operators have been heralded as key to the success of Graph Neural Networks (GNNs). Yet, despite the multiplication of GNN methods across tasks and…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…
Several indices used in a factor graph data structure can be permuted without changing the underlying probability distribution. An algorithm that performs inference on a factor graph should ideally be equivariant or invariant to…
Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database.…
Computed tomography (CT) is a widely used medical imaging technique to scan internal structures of a body, typically involving collimation and mechanical rotation. Compton scatter tomography (CST) presents an interesting alternative to…
We introduce Eff-GRot, an approach for efficient and generalizable rotation estimation from RGB images. Given a query image and a set of reference images with known orientations, our method directly predicts the object's rotation in a…