Related papers: Obstructions to Compositionality
We formalize human language understanding as a structured prediction task where the output is a partially ordered set (poset). Current encoder-decoder architectures do not take the poset structure of semantics into account properly, thus…
Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
Various concepts of grammatical compositionality arise in many theories of both natural and artificial languages, and often play a key role in accounts of the syntax-semantics interface. We propose that many instances of compositionality…
Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Primitive positive constructions have been introduced in recent work of Barto, Opr\v{s}al, and Pinsker to study the computational complexity of constraint satisfaction problems. Let $\mathfrak P_{\operatorname{fin}}$ be the poset which…
Categorical compositional distributional semantics is an approach to modelling language that combines the success of vector-based models of meaning with the compositional power of formal semantics. However, this approach was developed…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…
By default neural networks are not robust to changes in data distribution. This has been demonstrated with simple image corruptions, such as blurring or adding noise, degrading image classification performance. Many methods have been…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…