4 papers
Compositional Dynamics in Learning and Mechanics
David I. Spivak
We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics. The syntax is an operad Arr whose objects ar…
Organizing Physics with Open Energy-Driven Systems
Matteo Capucci, Owen Lynch, David I. Spivak
Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamilto…
Pattern Runs on Matter: The Free Monad Monad as a Module over the Cofree Comonad Comonad
Sophie Libkind, David I. Spivak
Interviews run on people, programs run on operating systems, voting schemes run on voters, games run on players. Each of these is an example of the abstraction pattern runs on matt…
Dynamic task delegation for hierarchical agents
Sophie Libkind, David I. Spivak
This is the fourth installment in a series of papers offering models of hierarchical structure for dynamical systems, using the language of polynomial functors. The operad underlyi…