10 papers
Convex Biproducts, Stochastic Matrices and Tape Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Categories with finite biproducts play a central role in category theory, providing an abstract setting in which additive and linear structures can be studied uniformly. In this pa…
Effectful Mealy Machines
Filippo Bonchi, Elena Di Lavore, Mario Román
Effectful Mealy machines, which we introduce, are a generalization of Mealy machines with global effects determined by an effectful triple. We provide semantics of effectful Mealy…
The calculus of neo-Peircean relations
Filippo Bonchi, Alessandro Di Giorgio, Nathan Haydon +1
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on qu…
Actionable Interpretability Must Be Defined in Terms of Symmetries
Pietro Barbiero, Mateo Espinosa Zarlenga, Francesco Giannini +4
This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpr…
The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics
Pietro Barbiero, Giovanni De Felice, Mateo Espinosa Zarlenga +5
As Artificial Intelligence models grow in complexity, interpretability has become an indispensable tool for understanding, debugging, and controlling their computations. However, i…
A Diagrammatic Basis for Computer Programming
Filippo Bonchi, Alessandro Di Giorgio, Elena Di Lavore
Tape diagrams provide a convenient graphical notation for arrows of rig categories, i.e., categories equipped with two monoidal products, and . In this work, we i…