2022/08/25 by Toby St Clere Smithe, Smithe, Toby St. Clere · 1 citation
Arts and Humanities · #Adaptation and Self-Organizing Systems (nlin.AO) #Artificial Intelligence (cs.AI) #Category Theory (math.CT) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Philosophy and History of Science #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2208.12173
openalex publication_date 2022/08/25 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit such functors, we first develop the necessary theory of dynamical systems, using a generalization of the language of polynomial functors to supply compositional interfaces of the required types: with the resulting polynomially indexed categories of coalgebras, we construct monoidal bicategories of differential and dynamical ``hierarchical inference systems'', in which approximate inference doctrines have semantics. We then describe ``externally parameterized'' statistical games, and use them to construct two approximate inference doctrines found in the computational neuroscience literature, which we call the `Laplace' and the `Hebb-Laplace' doctrines: the former produces dynamical systems which optimize the posteriors of Gaussian models; and the latter produces systems which additionally optimize the parameters (or `weights') which determine their predictions.