Related papers: Improving Hyperbolic Representations via Gromov-Wa…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…

The Wasserstein space of probability measures is known for its intricate Riemannian structure, which underpins the Wasserstein geometry and enables gradient flow algorithms. However, the Wasserstein geometry may not be suitable for certain…

Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…

We present a data-driven dimensionality reduction method that is well-suited for physics-based data representing hyperbolic wave propagation. The method utilizes a specialized neural network architecture called low rank neural…

In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…

We study typical distances in a geometric random graph on the hyperbolic plane. Introduced by Krioukov et al.~\cite{ar:Krioukov} as a model for complex networks, $N$ vertices are drawn randomly within a bounded subset of the hyperbolic…

Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…

We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. Due to meeting this theoretical underpinning, it is a…

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex…

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…

Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of…

Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…

Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…

We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to…

Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…

Hyperbolic Neural Networks (HNNs), operating in hyperbolic space, have been widely applied in recent years, motivated by the existence of an optimal embedding in hyperbolic space that can preserve data hierarchical relationships (termed…