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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…
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…
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…
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…
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…
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…
Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of…
Embedding methods for product spaces are powerful techniques for low-distortion and low-dimensional representation of complex data structures. Here, we address the new problem of linear classification in product space forms -- products of…
Hierarchical and tree-like data sets arise in many applications, including language processing, graph data mining, phylogeny and genomics. It is known that tree-like data cannot be embedded into Euclidean spaces of finite dimension with…
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…
Hyperbolic spaces have proven to be suitable for modeling data of hierarchical nature. As such we use the Poincare ball to embed sentences with the goal of proving how hyperbolic spaces can be used for solving Textual Entailment. To this…
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…
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 space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…
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…
We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is…
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…
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…
Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…