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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…

High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…

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…

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space…

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…

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however,…

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…

Knowledge graph embeddings (KGE) have been validated as powerful methods for inferring missing links in knowledge graphs (KGs) that they typically map entities into Euclidean space and treat relations as transformations of entities.…

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…

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…

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…

Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…

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…

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…

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The…