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Selective state-space models excel at long-sequence modeling, but their capacity for language representation -- in complex hierarchical reasoning -- remains underexplored. Most large language models rely on \textit{flat} Euclidean…
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…
Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…
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…
Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…
Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical…
Biomedical association studies are increasingly done using clinical concepts, and in particular diagnostic codes from clinical data repositories as phenotypes. Clinical concepts can be represented in a meaningful, vector space using word…
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…
In practice, many medical datasets have an underlying taxonomy defined over the disease label space. However, existing classification algorithms for medical diagnoses often assume semantically independent labels. In this study, we aim to…
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…
Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets.…
Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…
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…
The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…
Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models…
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…
Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image…
Large Language Models (LLMs) have attracted significant attention in recommender systems for their excellent world knowledge capabilities. However, existing methods that rely on Euclidean space struggle to capture the rich hierarchical…
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…
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…