Related papers: LaB-GATr: geometric algebra transformers for large…

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no…

The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…

Representation learning on large-scale unstructured volumetric and surface meshes poses significant challenges in neuroimaging, especially when models must incorporate diverse vertex-level morphometric descriptors, such as cortical…

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries…

Transformer-based models have improved predictive modeling on longitudinal electronic health records through large-scale self-supervised pretraining. However, most EHR transformer architectures treat each clinical encounter as an unordered…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

In the field of medical image, deep convolutional neural networks(ConvNets) have achieved great success in the classification, segmentation, and registration tasks thanks to their unparalleled capacity to learn image features. However,…

We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over…

Modelling the propagation of electromagnetic wireless signals is critical for designing modern communication systems. Wireless ray tracing simulators model signal propagation based on the 3D geometry and other scene parameters, but their…

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…

3D human mesh recovery from a 2D pose plays an important role in various applications. However, it is hard for existing methods to simultaneously capture the multiple relations during the evolution from skeleton to mesh, including…

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision,…

Deep learning affords enormous opportunities to augment the armamentarium of biomedical imaging, albeit its design and implementation have potential flaws. Fundamentally, most deep learning models are driven entirely by data without…

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…

Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

Mesh reconstruction is a cornerstone process across various applications, including in-silico trials, digital twins, surgical planning, and navigation. Recent advancements in deep learning have notably enhanced mesh reconstruction speeds.…

Advances in imaging methods such as electron microscopy, tomography and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for…