Related papers: Equivariant Maps for Hierarchical Structures
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…
Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for…
In addressing the challenge of Crystal Structure Prediction (CSP), symmetry-aware deep learning models, particularly diffusion models, have been extensively studied, which treat CSP as a conditional generation task. However, ensuring…
When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural…
Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the…
Numerous point-cloud understanding techniques focus on whole entities and have succeeded in obtaining satisfactory results and limited sparsity tolerance. However, these methods are generally sensitive to incomplete point clouds that are…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one…
We propose a new supervized learning framework for oversegmenting 3D point clouds into superpoints. We cast this problem as learning deep embeddings of the local geometry and radiometry of 3D points, such that the border of objects presents…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
In recent years, deep models have achieved remarkable success in various vision tasks. However, their performance heavily relies on large training datasets. In contrast, humans exhibit hybrid learning, seamlessly integrating structured…
Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any…
The ability to generate novel, diverse, and realistic 3D shapes along with associated part semantics and structure is central to many applications requiring high-quality 3D assets or large volumes of realistic training data. A key challenge…
The design of convolutional neural architectures that are exactly equivariant to continuous translations is an active field of research. It promises to benefit scientific computing, notably by making existing imaging systems more physically…
Classification and segmentation of 3D point clouds are important tasks in computer vision. Because of the irregular nature of point clouds, most of the existing methods convert point clouds into regular 3D voxel grids before they are used…