Related papers: Vector symbolic architectures for context-free gra…
In the field of computer graphics, the use of vector graphics, particularly Scalable Vector Graphics (SVG), represents a notable development from traditional pixel-based imagery. SVGs, with their XML-based format, are distinct in their…
Probabilistic context-free grammars (PCFGs) with neural parameterization have been shown to be effective in unsupervised phrase-structure grammar induction. However, due to the cubic computational complexity of PCFG representation and…
Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a…
Graph data model and graph databases are very popular in various areas such as bioinformatics, semantic web, and social networks. One specific problem in the area is a path querying with constraints formulated in terms of formal grammars.…
Many machine learning algorithms require the input to be represented as a fixed-length feature vector. When it comes to texts, one of the most common fixed-length features is bag-of-words. Despite their popularity, bag-of-words features…
A plethora of vector-space representations for words is currently available, which is growing. These consist of fixed-length vectors containing real values, which represent a word. The result is a representation upon which the power of many…
Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
Embedding large and high dimensional data into low dimensional vector spaces is a necessary task to computationally cope with contemporary data sets. Superseding latent semantic analysis recent approaches like word2vec or node2vec are well…
Context-dependent fusion grammars were recently introduced as devices for the generation of hypergraph languages. In this paper, we show that this new type of hypergraph grammars, where the application of fusion rules is restricted by…
Automatically discovering formulaic alpha factors is a central problem in quantitative finance. Existing methods often ignore syntactic and semantic constraints, relying on exhaustive search over unstructured and unbounded spaces. We…
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs…
Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we construct a Fock space and associated vertex operators in terms of representation ring of wreath products $\Gamma\sim S_n$. We recover the character tables of wreath…
The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…