Related papers: Two Embedding Theorems for Data with Equivalences …

Conventional text classification models make a bag-of-words assumption reducing text into word occurrence counts per document. Recent algorithms such as word2vec are capable of learning semantic meaning and similarity between words in an…

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…

Modeling place functions from a computational perspective is a prevalent research topic. Trajectory embedding, as a neural-network-backed dimension reduction technology, allows the possibility to put places with similar social functions at…

We propose to test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using manifold-learning techniques. In particular, we…

A variety of knowledge graph embedding approaches have been developed. Most of them obtain embeddings by learning the structure of the knowledge graph within a link prediction setting. As a result, the embeddings reflect only the structure…

Answering complex queries on knowledge graphs is important but particularly challenging because of the data incompleteness. Query embedding methods address this issue by learning-based models and simulating logical reasoning with set…

We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and…

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…

Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

A well-known theorem of Assouad states that metric spaces satisfying the doubling property can be snowflaked and bi-Lipschitz embedded into Euclidean spaces. Due to the invariance of many geometric properties under bi-Lipschitz maps, this…

A well-known result by Lindenstrauss is that any two-dimensional normed space can be isometrically imbedded into $L_1(0,1)$. We provide an explicit form of a such an imbedding. The proof is elementary and self-contained. Applications are…

The rapidly growing ecosystem of Large Language Models (LLMs) makes it increasingly challenging to manage and utilize the vast and dynamic pool of models effectively. We propose LOCUS, a method that produces low-dimensional vector…

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…

Word embeddings capture semantic relationships based on contextual information and are the basis for a wide variety of natural language processing applications. Notably these relationships are solely learned from the data and subsequently…

While the similarity between two concept words has been evaluated and studied for decades, much less attention has been devoted to algorithms that can compute the similarity of nodes in very large knowledge graphs, like Wikidata. To…

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…

We explore in depth how categorical data can be processed with embeddings in the context of claim severity modeling. We develop several models that range in complexity from simple neural networks to state-of-the-art attention based…