Related papers: Representation Embeddings of Cartesian Theories
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…
For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…
By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…
We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a…
We introduce the first method for translating text embeddings from one vector space to another without any paired data, encoders, or predefined sets of matches. Our unsupervised approach translates any embedding to and from a universal…
The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is…
We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained with induction from a discrete series representation of a parabolic subalgebra. We determine all…
We construct the E theory analogue of the particles that transform under the Poincare group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of E11 with its vector representation. We…