相关论文: Comparing Euclidean and Hyperbolic K-Means for Gen…

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…

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with…

Taxonomies are valuable resources for many applications, but the limited coverage due to the expensive manual curation process hinders their general applicability. Prior works attempt to automatically expand existing taxonomies to improve…

Generalized Category Discovery (GCD) aims to discover novel categories in unlabelled datasets using knowledge learned from labelled samples. Previous studies argued that parametric classifiers are prone to overfitting to seen categories,…

Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides…

Many AI-related tasks involve the interactions of data in multiple modalities. It has been a new trend to merge multi-modal information into knowledge graph(KG), resulting in multi-modal knowledge graphs (MMKG). However, MMKGs usually…

Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden…

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image…

Generalized Category Discovery (GCD) aims to identify novel categories in unlabeled data while leveraging a small labeled subset of known classes. Training a parametric classifier solely on image features often leads to overfitting to old…

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…

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…

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…

The hyperbolic space, characterized by a constant negative curvature and exponentially expanding space, aligns well with the structural properties of heterogeneous graphs. However, although heterogeneous graphs inherently possess diverse…

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

Accurate brain tumor classification is critical for intra-operative decision making in neuro-oncological surgery. However, existing approaches are restricted to a fixed set of predefined classes and are therefore unable to capture patterns…

Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hyperbolic space has recently gained rapid traction for learning…

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…

Generalized Category Discovery (GCD) utilizes labeled samples of known classes to discover novel classes in unlabeled samples. Existing methods show effective performance on artificial datasets with balanced distributions. However,…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

We prove an exponential separation in sample complexity between Euclidean and hyperbolic representations for learning on hierarchical data under standard Lipschitz regularization. For depth-$R$ hierarchies with branching factor $m$, we…