Uncovering the mechanisms of physics is driving a new paradigm in artificial intelligence
(AI) discovery. Today, physics has enabled us to understand the AI paradigm in a wide …

Symmetric Positive Definite (SPD) matrices have received wide attention in machine
learning due to their intrinsic capacity to encode underlying structural correlation in data …

Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data
structures prevalent in real-world datasets. Notably, residual connections, which facilitate the …

Normalization and residual connections find extensive application within the intricate
architecture of deep neural networks, contributing significantly to their heightened …

Riemannian neural networks, which extend deep learning techniques to Riemannian
spaces, have gained significant attention in machine learning. To better classify the manifold …

We propose two graph neural network layers for graphs with features in a Riemannian
manifold. First, based on a manifold-valued graph diffusion equation, we construct a …

In this paper we develop a manifestly geometric framework for equivariant manifold neural
ordinary differential equations (NODEs), and use it to analyse their modelling capabilities for …

Recent papers in the graph machine learning literature have introduced a number of
approaches for hyperbolic representation learning. The asserted benefits are improved …

Signature, lying at the heart of rough path theory, is a central tool for analysing controlled
differential equations driven by irregular paths. Recently it has also found extensive …

Although machine learning researchers have introduced a plethora of useful constructions
for learning over Euclidean space, numerous types of data found in various applications …