Da Costa Lancelot, Friston Karl, Heins Conor, Pavliotis Grigorios A
Department of Mathematics, Imperial College London, London SW7 2AZ, UK.
Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3AR, UK.
Proc Math Phys Eng Sci. 2021 Dec;477(2256):20210518. doi: 10.1098/rspa.2021.0518. Epub 2021 Dec 8.
This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.
本文为自适应系统开发了一种贝叶斯力学。首先，我们用马尔可夫毯对系统与其环境之间的界面进行建模。这提供了一些条件，在这些条件下，毯内部的状态编码有关外部状态的信息。其次，我们引入动力学，并将自适应系统表示为稳态下的马尔可夫毯。这使我们能够识别出一大类系统，其内部状态似乎在推断外部状态，这与贝叶斯统计学和理论神经科学中的变分推断一致。最后，我们将毯划分为感觉状态和主动状态。由此可见，主动状态可被视为执行主动推断和著名的随机控制形式（如PID控制），这些是理论生物学和工程中自适应行为的突出表述。
