22 citations · 103 across the 26 of their papers we have counts for
10 papers · 1 filter
The Compositional Structure of Bayesian Inference
Dylan Braithwaite, Jules Hedges, Toby St Clere Smithe
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, w…
Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion
Dylan Braithwaite, Jules Hedges
We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpr…
Value Iteration is Optic Composition
Jules Hedges, Riu Rodríguez Sakamoto
Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is als…
Fibre optics
Dylan Braithwaite, Matteo Capucci, Bruno Gavranović +2
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied categor…
Towards Foundations of Categorical Cybernetics
Matteo Capucci, Bruno Gavranović, Jules Hedges +1
We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller…
Sheet diagrams for bimonoidal categories
Cole Comfort, Antonin Delpeuch, Jules Hedges
Bimonoidal categories (also known as rig categories) are categories with two monoidal structures, one of which distributes over the other. We formally define sheet diagrams, a grap…
Foundations of brick diagrams
Jules Hedges, Jelle Herold
We discuss the foundations of 2-dimensional graphical languages, with a view towards their computer implementation in a 'compiler' for monoidal categories. In particular, we discus…
From open learners to open games
Jules Hedges
The categories of open learners (due to Fong, Spivak and Tuyéras) and open games (due to the present author, Ghani, Winschel and Zahn) bear a very striking and unexpected similarit…
Limits of bimorphic lenses
Jules Hedges
Bimorphic lenses are a simplification of polymorphic lenses that (like polymorphic lenses) have a type defined by 4 parameters, but which are defined in a monomorphic type system (…
Coherence for lenses and open games
Jules Hedges
Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but…