On Markov blankets and hierarchical self-organisation

Ensor Rafael Palacios,Adeel Razi,Thomas Parr,Michael Kirchhoff,Karl Friston

doi:10.1016/j.jtbi.2019.110089

Abstract

Biological self-organisation can be regarded as a process of spontaneous pattern formation; namely, the emergence of structures that distinguish themselves from their environment. This process can occur at nested spatial scales: from the microscopic (e.g., the emergence of cells) to the macroscopic (e.g. the emergence of organisms). In this paper, we pursue the idea that Markov blankets – that separate the internal states of a structure from external states – can self-assemble at successively higher levels of organisation. Using simulations, based on the principle of variational free energy minimisation, we show that hierarchical self-organisation emerges when the microscopic elements of an ensemble have prior (e.g., genetic) beliefs that they participate in a macroscopic Markov blanket: i.e., they can only influence – or be influenced by – a subset of other elements. Furthermore, the emergent structures look very much like those found in nature (e.g., cells or organelles), when influences are mediated by short range signalling. These simulations are offered as a proof of concept that hierarchical self-organisation of Markov blankets (into Markov blankets) can explain the self-evidencing, autopoietic behaviour of biological systems.

Highlights

There is growing interest in the role of Markov blankets and associated partitions in understanding self-organisation– and the accompanying self-evidencing that arises from Bayesian mechanics (Friston, 2019)
Our primary aim was to show that hierarchal compositions of Markov blankets of Markov blankets can emerge from gradient flows on variational free energy, under an appropriate generative model
We provide an intuition on the chief role that Markov blankets have in self-organisation within the free energy principle

Summary

Introduction

There is growing interest in the role of Markov blankets and associated partitions in understanding self-organisation– and the accompanying self-evidencing that arises from Bayesian mechanics (Friston, 2019). A key aspect of this self-organisation is the hierarchical decomposition of Markov blankets of Markov blankets. This notion has emerged in the literature at several levels; ranging from conceptual analyses in the context of ethology and evolution (Allen, 2018; Clark, 2017; Friston et al, 2015; Kirchhoff et al, 2018; Pellet and Elisseeff, 2008; Ramstead et al, 2018), through to the emergence of multicellular organisms (Kuchling et al, 2019) to the implicit renormalisation group that furnishes a particular perspective on (quantum, statistical and classical) mechanics (Friston, 2019; Friston et al, 2014). Our primary aim was to show that hierarchal compositions of Markov blankets of Markov blankets can emerge from gradient flows on variational free energy, under an appropriate generative model

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Conclusion