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In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are…
Implicit Neural Representations (INRs) are widely used for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Architectures such as SIREN, WIRE, and FINER demonstrate their ability to…
Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Recent advances in generative models for medical imaging have shown promise in representing multiple modalities. However, the variability in modality availability across datasets limits the general applicability of the synthetic data they…
Recent work has shown the ability to learn generative models for 3D shapes from only unstructured 2D images. However, training such models requires differentiating through the rasterization step of the rendering process, therefore past work…
Gravitational form factors (GFFs), defined through the matrix elements of the energy-momentum tensor, provide critical insights into the internal structure of nucleons and nuclei. In particular, their Fourier transforms -- evaluated in the…
Generative models for 2D images has recently seen tremendous progress in quality, resolution and speed as a result of the efficiency of 2D convolutional architectures. However it is difficult to extend this progress into the 3D domain since…
Realistic human geometry generation is an important yet challenging task, requiring both the preservation of fine clothing details and the accurate modeling of clothing-body interactions. To tackle this challenge, we build upon Geometry…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
Materials discovery is fundamental to advance next-generation technologies as well as for sustainable and circular economy. Beyond computational screening, generative models are efficient at finding materials with desired properties, via…
Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the…
Current generative frameworks use end-to-end learning and generate images by sampling from uniform noise distribution. However, these approaches ignore the most basic principle of image formation: images are product of: (a) Structure: the…
Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers typically produce a single solution only and rely on local search techniques to…
Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…
Rapid advancements in medical image segmentation performance have been significantly driven by the development of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs). These models follow the discriminative pixel-wise…
Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular…
3D Gaussian Splatting (3DGS) has demonstrated superior quality in modeling 3D objects and scenes. However, generating 3DGS remains challenging due to their discrete, unstructured, and permutation-invariant nature. In this work, we present a…
Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements…
A Computer-Aided Design (CAD) model encodes an object in two coupled forms: a parametric construction sequence and its resulting visible geometric shape. During iterative design, adjustments to the geometric shape inevitably require…