Related papers: Towards Non-Euclidean Foundation Models: Advancing…

Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many…

Hyperbolic space can naturally embed hierarchies, unlike Euclidean space. Hyperbolic Neural Networks (HNNs) exploit such representational power by lifting Euclidean features into hyperbolic space for classification, outperforming Euclidean…

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved),…

Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…

In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual…

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…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

Trajectory similarity is a cornerstone of trajectory data management and analysis. Traditional similarity functions often suffer from high computational complexity and a reliance on specific distance metrics, prompting a shift towards deep…

Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…

The prevalence of tree-like structures, encompassing hierarchical structures and power law distributions, exists extensively in real-world applications, including recommendation systems, ecosystems, financial networks, social networks, etc.…

Machine learning models that embed graphs in non-Euclidean spaces have shown substantial benefits in a variety of contexts, but their application has not been studied extensively in the biological domain, particularly with respect to…

While the exploration for embodied AI has spanned multiple decades, it remains a persistent challenge to endow agents with human-level intelligence, including perception, learning, reasoning, decision-making, control, and generalization…