Related papers: Poincar\'e Embeddings for Learning Hierarchical Re…
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 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…
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…
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…
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…
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…
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…
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…
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…
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…
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…
Natural language text exhibits hierarchical structure in a variety of respects. Ideally, we could incorporate our prior knowledge of this hierarchical structure into unsupervised learning algorithms that work on text data. Recent work by…
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 task-specific representations of persistence diagrams is an important problem in topological data analysis and machine learning. However, current state of the art methods are restricted in terms of their expressivity as they are…
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 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…
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to…
The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…
Cross-lingual word embeddings can be applied to several natural language processing applications across multiple languages. Unlike prior works that use word embeddings based on the Euclidean space, this short paper presents a simple and…