12 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…
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…
Tapes as Stochastic Matrices of String Diagrams
Filippo Bonchi, Cipriano Junior Cioffo
Tape diagrams provide a graphical notation for categories equipped with two monoidal products, and , where is a biproduct. Recently, they have been gener…
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…
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…
Deriving Program Logics from Distributive Monoidal Categories
Filippo Bonchi, Elena Di Lavore, Mario Román +1
We derive multiple program logics - including correctness, incorrectness, and relational Hoare logic - from the axioms of imperative categories: uniformly traced distributive copy-…
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…
Tape Diagrams for Monoidal Monads
Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio +1
Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, and , where dist…
Mathematical Foundation of Interpretable Equivariant Surrogate Models
Jacopo Joy Colombini, Filippo Bonchi, Francesco Giannini +3
This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant…
A Diagrammatic Algebra for Program Logics
Filippo Bonchi, Alessandro Di Giorgio, Elena Di Lavore
Tape diagrams provide a convenient notation for arrows of rig categories, i.e., categories equipped with two monoidal products, and , where distributes…
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…
When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines
Filippo Bonchi, Alessandro Di Giorgio, Davide Trotta
Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and comple…