Related papers: Improving Local Identifiability in Probabilistic B…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved),…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

We show that the predicted probability distributions for any $N$-parameter statistical model taking the form of an exponential family can be explicitly and analytically embedded isometrically in a $N{+}N$-dimensional Minkowski space. That…

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,…

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…

Researchers have recently suggested that models share common representations. In our work, we find numerous geometric similarities across the token embeddings of large language models. First, we find ``global'' similarities: token…

Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…

Analysis of word embedding properties to inform their use in downstream NLP tasks has largely been studied by assessing nearest neighbors. However, geometric properties of the continuous feature space contribute directly to the use of…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a fuzzy representation of object regions using Gaussian distributions, which provides an implicit binary…

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…

The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…

Knowledge graph embeddings (KGE) have been extensively studied to embed large-scale relational data for many real-world applications. Existing methods have long ignored the fact many KGs contain two fundamentally different views: high-level…

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…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…