Related papers: Compatibility support mappings in effect algebras
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Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph…
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Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
I present a generalized notion of obstruction in \v{C}ech cohomology on semi-modules, which allows one to characterize non-disturbing contextual behaviors with any semi-field. This framework generalizes the usual \v{C}ech cohomology used in…
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…
In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
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Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…
We present a method for identifying groups of test examples -- slices -- on which a model under-performs, a task now known as slice discovery. We formalize coherence -- a requirement that erroneous predictions, within a slice, should be…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation…
Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction,…
Concept embeddings offer a practical and efficient mechanism for injecting commonsense knowledge into downstream tasks. Their core purpose is often not to predict the commonsense properties of concepts themselves, but rather to identify…
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Previous research on word embeddings has shown that sparse representations, which can be either learned on top of existing dense embeddings or obtained through model constraints during training time, have the benefit of increased…