Related papers: An excursion into Dialectica and Differentiation
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
I would like to tell a story. A story about a beautiful mathematical relationship that elucidates the computational view on the classic subject of trigonometry. All stories need a language, and for this particular story an algorithmic…
In this paper, it is proved that dictionary learning and sparse representation is invariant to a linear transformation. It subsumes the special case of transforming/projecting the data into a discriminative space. This is important because…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which…
Propelling, and propelled by, the "deep learning revolution", recent years have seen the introduction of ever larger corpora of images annotated with natural language expressions. We survey some of these corpora, taking a perspective that…
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…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
Our languages are in constant flux driven by external factors such as cultural, societal and technological changes, as well as by only partially understood internal motivations. Words acquire new meanings and lose old senses, new words are…
The concept of a temporal phylogenetic network is a mathematical model of evolution of a family of natural languages. It takes into account the fact that languages can trade their characteristics with each other when linguistic communities…
Referring expression comprehension aims to localize objects identified by natural language descriptions. This is a challenging task as it requires understanding of both visual and language domains. One nature is that each object can be…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…