Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to
find the low-dimensional structure of data. Dimension reduction for large, high-dimensional …

Cellular sheaves equip graphs with a``geometrical''structure by assigning vector spaces and
linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph …

Abstract Graph Neural Networks (GNNs) are limited in their expressive power, struggle with
long-range interactions and lack a principled way to model higher-order structures. These …

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for
elucidating the three-dimensional (3D) structure of proteins and other biologically significant …

We present a novel, end-to-end learnable, multiview 3D point cloud registration algorithm.
Registration of multiple scans typically follows a two-stage pipeline: the initial pairwise …

Many important geometric estimation problems naturally take the form of synchronization
over the special Euclidean group: estimate the values of a set of unknown group elements x …

We present a novel representation of maps between pairs of shapes that allows for efficient
inference and manipulation. Key to our approach is a generalization of the notion of map …

Abstract A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that
operates on a sheaf, an object that equips a graph with vector spaces over its nodes and …

Constrained by the limitations of learning toolkits engineered for other applications, such as
those in image processing, many mesh-based learning algorithms employ data flows that …

Point cloud registration is a fundamental task in computer graphics, and more specifically, in
rigid and non-rigid shape matching. The rigid shape matching problem can be formulated as …