9 papers
A Diagrammatic Axiomatisation of Behavioural Distance of Nondeterministic Processes
Wojciech Różowski, Robin Piedeleu, Alexandra Silva +1
Behavioural distances provide a quantitative approach to comparing the states of transition systems, moving beyond traditional Boolean notions of equivalence. In this paper, we dev…
Complete Diagrammatic Axiomatisations of Relative Entropy
Ralph Sarkis, Fabio Zanasi
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In thi…
Layered Monoidal Theories II: Fibrational Semantics
Leo Lobski, Fabio Zanasi
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models…
Layered Monoidal Theories I: Diagrammatic Algebra and Applications
Leo Lobski, Fabio Zanasi
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation…
Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective
Antonio Lorenzin, Fabio Zanasi
Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to…
Approaching the Continuous from the Discrete: an Infinite Tensor Product Construction
Antonio Lorenzin, Fabio Zanasi
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categor…
Logic Explanation of AI Classifiers by Categorical Explaining Functors
Stefano Fioravanti, Francesco Giannini, Paolo Frazzetto +2
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most…
An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models
Antonio Lorenzin, Fabio Zanasi
Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to…
Graded String Diagrams for Imprecise Probability and Causal Intervention
Ralph Sarkis, Fabio Zanasi
We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic…