Related papers: Kleisli semantics and hypergraph composition for G…
Humans understand new combinations of words encountered if they are combinations of words recognized from different contexts, an ability called Compositional Generalization. The COGS benchmark (Kim and Linzen, 2020) arXiv:2010.05465 reports…
Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…
We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent…
Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Reader reviews of literary fiction on social media, especially those in persistent, dedicated forums, create and are in turn driven by underlying narrative frameworks. In their comments about a novel, readers generally include only a subset…
Representing structured text from complex documents typically calls for different machine learning techniques, such as language models for paragraphs and convolutional neural networks (CNNs) for table extraction, which prohibits drawing…
This study investigates the diverse characteristics of nouns, focusing on both semantic (e.g., countable/uncountable) and morphosyntactic (e.g., masculine/feminine) distinctions. We explore inter-word variations for gender markers in noun…
We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these…
We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…
The category Rel of sets and relations intimately ties the notions of function, partial multivalued function, and direct image under a function through the description of Rel as the Kleisli category of the covariant power set functor on…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…
We introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
The paper presents an enhancement of xASP, a system that generates explanation graphs for Answer Set Programming (ASP). Different from xASP, the new system, xASP2, supports different clingo constructs like the choice rules, the constraints,…
We construct explicitly the weights on the simplicial category so that the colimits and limits of 2-functors with those weights provide the Kleisli objects and the Eilenberg-Moore objects, respectively, in any 2-category.
A formal description of the compositionality of neural networks is associated directly with the formal grammar-structure of the objects it seeks to represent. This formal grammar-structure specifies the kind of components that make up an…
We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…