The Markov blankets of life: autonomy, active inference and the free energy principle

These examples both show that the organizational boundaries of living systems are open and flexible in the precise sense that such boundaries need not be co-extensive with an organism's bodily boundaries.

In this paper we have argued that the autonomous organization of living systems consists of the hierarchical assembly of Markov blankets of Markov blankets through adaptive active inference. We have further argued that this nested Markov blanketed organization need not be co-extensive with the biophysical boundaries of the organism but may extend to include aspects of an organism's environment. We have not established (i.e. shown) that the self-organization of hierarchically composed Markov blankets of Markov blankets is an emergent property of systems (under the right sorts of conditions). Our focus in this paper has been on the implications of such an emergent structure. Having said this, in a parallel (formal) programme of work, we have used simulations to provide a proof of principle that this particular (and possible ubiquitous) form of self-organization is an emergent property. The simulations we use in this parallel work build on previous work that characterizes the emergence of pattern formation and morphogenesis in a biological system [7] but with an important twist. Instead of simulating the assembly of Markov blankets systems from the bottom up, we apply a top-down approach (see Palacios et al. [46] for details).

We would like to thank Ian Robertson for providing us with detailed comments on an earlier draft of this manuscript. We would also like to thank Jelle Bruineberg for fruitful discussions during the writing of this work.

The curve of a logarithmic function is concave. This has an important implication when averages are taken either of the logarithmic function or of the input to the function. To gain some intuition for this, consider a dataset of just two points, x1 and x2. The average of these will lie halfway between the two, as shown on the x-axis in figure 5. When the logarithms of x1, x2 and their average are calculated (y-axis), it is clear that the log of the average lies above the midpoint between logx1 and logx2. The midpoint is the average of the logarithms, so this implies that the log of an average is greater than the average of a log. This is a statement of Jensen's inequality.

If we replace the variable x with a ratio of probabilities, , and take averages (‘expectations’) with respect to a distribution Q(s), we can use Jensen's inequality to write:

The term on the left (the average of the log) is the negative free energy. The term on the right is the negative surprise. To see this, if we write the expectation out in full, we have

These allow us to rewrite the inequality (noting that, when we make both sides negative, the inequality sign reverses),

All the authors contributed to the writing of this work and participated in discussions on the basis of their expertise, which led to the concepts and critical points mentioned here. M.K. and K.F. wrote and edited the manuscript. T.P. contributed with details on the mathematical aspects throughout the review and appendix A. E.P. and J.K. made significant editorial and corrective work on the review reported here.

We are grateful for the support of the John Templeton Foundation (M.K. is funded by a John Templeton Foundation Academic Cross-Training Fellowship (ID no. 60708)), the Australian Research Council (M.K. is funded by an Australian Research Council Discovery Project (DP170102987)), the Wellcome Trust (K.F. is funded by a Wellcome Trust Principal Research Fellowship (ref: 088130/Z/09/Z)), the Rosetrees Trust (T.P. is funded by the Rosetrees Trust (173346)), and the European Research Council (J.K. is funded by the European Research Council in the form of a starting grant awarded to Erik Rietveld (679190)).