Related papers: Low-rank approximations of hyperbolic embeddings

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

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 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…

With the tremendous success of deep learning in visual tasks, the representations extracted from intermediate layers of learned models, that is, deep features, attract much attention of researchers. Previous empirical analysis shows that…

Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent…

We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results…

Learning accurate drug representations is essential for task such as computational drug repositioning. A drug hierarchy is a valuable source that encodes knowledge of relations among drugs in a tree-like structure where drugs that act on…

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…

We show that it is possible to reduce a high-dimensional object like a neural network agent into a low-dimensional vector representation with semantic meaning that we call agent embeddings, akin to word or face embeddings. This can be done…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory,…

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also…

Samples from intimate (non-linear) mixtures are generally modeled as being drawn from a smooth manifold. Scenarios where the data contains multiple intimate mixtures with some constituent materials in common can be thought of as manifolds…

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit…

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…

Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…