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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 geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks…

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…

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…

The exponential volume growth of hyperbolic geometry can embed the hierarchical relationships between states in reinforcement learning (RL) with far less distortion than Euclidean space. However, hyperbolic deep RL faces severe optimization…

The emergence of Deep Convolutional Neural Networks (DCNNs) has been a pervasive tool for accomplishing widespread applications in computer vision. Despite its potential capability to capture intricate patterns inside the data, the…

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…

Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…

Continual learning has traditionally focused on classifying either instances or classes, but real-world applications, such as robotics and self-driving cars, require models to handle both simultaneously. To mirror real-life scenarios, we…

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…

Hyperbolic Neural Networks (HNNs), operating in hyperbolic space, have been widely applied in recent years, motivated by the existence of an optimal embedding in hyperbolic space that can preserve data hierarchical relationships (termed…

Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…

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…

The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature…

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…

This work presents a reformulation of the recently proposed Wasserstein autoencoder framework on a non-Euclidean manifold, the Poincar\'e ball model of the hyperbolic space. By assuming the latent space to be hyperbolic, we can use its…

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,…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

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…