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The standard approach to incorporate linguistic information to neural machine translation systems consists in maintaining separate vocabularies for each of the annotated features to be incorporated (e.g. POS tags, dependency relation…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…
Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to…
Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Multi-tildes are regular operators that were introduced to enhance the factorization power of regular expressions, allowing us to add the empty word in several factors of a catenation product of languages. In addition to multi-bars, which…
Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
Distributed word representations have been demonstrated to be effective in capturing semantic and syntactic regularities. Unsupervised representation learning from large unlabeled corpora can learn similar representations for those words…
Word feature vectors have been proven to improve many NLP tasks. With recent advances in unsupervised learning of these feature vectors, it became possible to train it with much more data, which also resulted in better quality of learned…
Data-driven representation learning for words is a technique of central importance in NLP. While indisputably useful as a source of features in downstream tasks, such vectors tend to consist of uninterpretable components whose relationship…
Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders…
Semantic Similarity is an important application which finds its use in many downstream NLP applications. Though the task is mathematically defined, semantic similarity's essence is to capture the notions of similarity impregnated in humans.…
Weighted automata is a basic tool for specification in quantitative verification, which allows to express quantitative features of analysed systems such as resource consumption. Quantitative specification can be assisted by automata…
Generating explanations for neural networks has become crucial for their applications in real-world with respect to reliability and trustworthiness. In natural language processing, existing methods usually provide important features which…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…