Related papers: Hyperbolic vs Euclidean Embeddings in Few-Shot Lea…

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

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…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. Due to the constant negative curvature, the hyperbolic space resembles tree metrics and captures the…

Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability…

Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly…

Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often…

Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…

Learning and generalizing from limited examples, i,e, few-shot learning, is of core importance to many real-world vision applications. A principal way of achieving few-shot learning is to realize an embedding where samples from different…

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…

Many high-dimensional and large-volume data sets of practical relevance have hierarchical structures induced by trees, graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional…

Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed…

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…

Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…

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…

Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…