With the advances of data-driven machine learning research, a wide variety of prediction
problems have been tackled. It has become critical to explore how machine learning and …

Recently, hyperbolic deep neural networks (HDNNs) have been gaining momentum as the
deep representations in the hyperbolic space provide high fidelity embeddings with few …

Extracting robust and general 3D local features is key to downstream tasks such as point
cloud registration and reconstruction. Existing learning-based local descriptors are either …

Conventional neural architectures for sequential data present important limitations.
Recurrent networks suffer from exploding and vanishing gradients, small effective memory …

We present simplicial neural networks (SNNs), a generalization of graph neural networks to
data that live on a class of topological spaces called simplicial complexes. These are natural …

Physics-informed machine learning (PIML), referring to the combination of prior knowledge
of physics, which is the high level abstraction of natural phenomenons and human …

We survey the mathematical foundations of geometric deep learning, focusing on group
equivariant and gauge equivariant neural networks. We develop gauge equivariant …

Spatio-temporal forecasting is challenging attributing to the high nonlinearity in temporal
dynamics as well as complex location-characterized patterns in spatial domains, especially …

Equivariant networks capture the inductive bias about the symmetry of the learning task by
building those symmetries into the model. In this paper, we study how equivariance relates …

In panorama understanding, the widely used equirectangular projection (ERP) entails
boundary discontinuity and spatial distortion. It severely deteriorates the conventional CNNs …