Related papers: Super Rough Semantics
The notion of surreal number was introduced by J.H. Conway in the mid 1970's: the surreal numbers constitute a linearly ordered (proper) class $No$ containing the class of all ordinal numbers ($On$) that, working within the background set…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
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 text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…
We consider a set-theoretic version of mereology based on the inclusion relation $\subseteq$ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of $\in$ from $\subseteq$, we identify…
Let $(U, R)$ be an approximation space with $U$ being non-empty set and $R$ being an equivalence relation on $U$, and let $\overline{G}$ and $\underline{G}$ be the upper approximation and the lower approximation of subset $G$ of $U$. A…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We tackle the task of semantic alignment where the goal is to compute dense semantic correspondence aligning two images depicting objects of the same category. This is a challenging task due to large intra-class variation, changes in…
In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…
Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…
Human environments contain numerous objects configured in a variety of arrangements. Our goal is to enable robots to repose previously unseen objects according to learned semantic relationships in novel environments. We break this problem…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
Rough Set based concepts of Span and Spanning Sets were recently proposed to deal with uncertainties in data. Here, this paper, presents novel concepts for generic decision-making process using Rough Set based span for a decision table.…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
We construct a hierarchy of supersymmetric string theories by showing that the general N-extended superstrings may be viewed as a special class of the (N+1)-extended superstrings. As a side result, we find a twisted (N+2) superconformal…
This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…
Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the…