Related papers: Kleisli semantics and hypergraph composition for G…
Graphs are a highly expressive data structure, but it is often difficult for humans to find patterns from a complex graph. Hence, generating human-interpretable sequences from graphs have gained interest, called graph2seq learning. It is…
Following our recent development of a compositional model checking algorithm for Markov decision processes, we present a compositional framework for solving mean payoff games (MPGs). The framework is derived from category theory,…
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these…
The task of natural language inference (NLI) asks whether a given premise (expressed in NL) entails a given NL hypothesis. NLI benchmarks contain human ratings of entailment, but the meaning relationships driving these ratings are not…
A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of…
We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in…
Recent advances in text-to-speech, particularly those based on Graph Neural Networks (GNNs), have significantly improved the expressiveness of short-form synthetic speech. However, generating human-parity long-form speech with high dynamic…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
We present a hierarchical knowledge graph framework for the structured semantic understanding of visual narratives, using comics as a representative domain for multimodal storytelling. The framework organizes narrative content across three…
Graph-matching metrics such as Smatch are the de facto standard for evaluating neural semantic parsers, yet they capture surface overlap rather than logical equivalence. We reassess evaluation by pairing graph-matching with automated…
We address here the treatment of metonymic expressions from a knowledge representation perspective, that is, in the context of a text understanding system which aims to build a conceptual representation from texts according to a domain…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
We introduce a hierarchical categorical framework for Schema-Based Learning (SBL) structured across four interconnected levels. At the schema level, a free multicategory $Sch_{syn}$ encodes fundamental schemas and transformations. An…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
Knowledge Graphs (KG) constitute a flexible representation of complex relationships between entities particularly useful for biomedical data. These KG, however, are very sparse with many missing edges (facts) and the visualisation of the…
Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the…
AM dependency parsing is a method for neural semantic graph parsing that exploits the principle of compositionality. While AM dependency parsers have been shown to be fast and accurate across several graphbanks, they require explicit…
Kleisli categories have long been recognised as a setting for modelling the linear behaviour of various types of systems. However, the final coalgebra in such settings does not, in general, correspond to a fixed notion of linear semantics.…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural…