Deep representation learning is a ubiquitous part of modern computer vision. While
Euclidean space has been the de facto standard manifold for learning visual …

Finding meaningful representations and distances of hierarchical data is important in many
fields. This paper presents a new method for hierarchical data embedding and distance. Our …

Contemporary advances in the field of deep learning have embarked upon an exploration of
the underlying geometric properties of data, thus encouraging the investigation of …

Large language models (LLMs) have demonstrated remarkable performance on various
tasks. However, it remains an open question whether the default Euclidean space is the …

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures,
which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic …

We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space
consists of a set of Gaussian distributions. It is known that the set of the univariate Gaussian …

We propose HyperSteiner–an efficient heuristic algorithm for computing Steiner minimal
trees in the hyperbolic space. HyperSteiner extends the Euclidean Smith-Lee-Liebman …

Since the publication of CLIP, the approach of using InfoNCE loss for contrastive pre-training
has become widely popular for bridging two or more modalities. Despite its wide adoption …

Optimal Transport has received much attention in Machine Learning as it allows to compare
probability distributions by exploiting the geometry of the underlying space. However, in its …

We propose the idea of using Kuramoto models (including their higher-dimensional
generalizations) for machine learning over non-Euclidean data sets. These models are …