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Distributional semantics models derive word space from linguistic items in context. Meaning is obtained by defining a distance measure between vectors corresponding to lexical entities. Such vectors present several problems. In this paper…
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…
Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension $k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove that for $k\ge3$ odd $K$ embeds into $M$ if and only if there are $\bullet$ a…
Knowledge Graph Embedding (KGE) is a common approach for Knowledge Graphs (KGs) in AI tasks. Embedding dimensions depend on application scenarios. Requiring a new dimension means training a new KGE model from scratch, increasing cost and…
Low dimensional embeddings that capture the main variations of interest in collections of data are important for many applications. One way to construct these embeddings is to acquire estimates of similarity from the crowd. However,…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
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…
Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…
We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the…
We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…
The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship…
A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches are focused on reduction…
Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…
We study the problem of approximating the cone of positive semidefinite (PSD) matrices with a cone that can be described by smaller-sized PSD constraints. Specifically, we ask the question: "how closely can we approximate the set of…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these…
Text embedding models serve as a fundamental component in real-world search applications. By mapping queries and documents into a shared embedding space, they deliver competitive retrieval performance with high efficiency. However, their…
High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…