Related papers: Version Space Algebras are Acyclic Tree Automata

The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…

Timbre spaces have been used in music perception to study the perceptual relationships between instruments based on dissimilarity ratings. However, these spaces do not generalize to novel examples and do not provide an invertible mapping,…

Geospatial analysis lacks methods like the word vector representations and pre-trained networks that significantly boost performance across a wide range of natural language and computer vision tasks. To fill this gap, we introduce Tile2Vec,…

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…

We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere…

Vectorization is a compiler optimization that replaces multiple operations on scalar values with a single operation on vector values. Although common in traditional compilers such as rustc, clang, and gcc, vectorization is not common in the…

In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we…

The application of machine learning algorithms to source code has grown in the past years. Since these algorithms are quite sensitive to input data, it is not surprising that researchers experiment with input representations. Nowadays, a…

Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by…

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…

In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is…

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…

In the field of natural language processing (NLP), continuous vector representations are crucial for capturing the semantic meanings of individual words. Yet, when it comes to the representations of sets of words, the conventional…

This article introduces a novel approach to spatial database design. Instead of extending the canonical Solid-Face-Edge-Vertex schema by, say, "hypersolids" these classes are generalised to a common type SpatialEntity, and the individual…

Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…

The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…

Visualization and topic modeling are widely used approaches for text analysis. Traditional visualization methods find low-dimensional representations of documents in the visualization space (typically 2D or 3D) that can be displayed using a…

Time-series of persistence diagrams, known as vineyards, have shown to be useful in diverse applications. A natural algebraic version of vineyards is a time series of persistence modules equipped with interleaving maps between the…

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR)…

We define guarded variable automata (GVAs), a simple extension of finite automata over infinite alphabets. In this model the transitions are labelled by letters or variables ranging over an infinite alphabet and guarded by conjunction of…