论文标题
对自由能原理某些部分的技术批评
A Technical Critique of Some Parts of the Free Energy Principle
论文作者
论文摘要
我们总结了自由能原理的原始表述,并突出了一些技术问题。我们讨论这些问题如何影响涉及广义坐标的相关结果,并在适当的情况下提到并揭示的后果,直到现在未被确认,这与自由能原理的新表述有所不同。特别是,我们揭示了不同作品中提出的“马尔可夫毛毯”的各种定义并不等效。我们表明,自由能力论证中的关键步骤涉及重写带有马尔可夫毛毯的系统运动方程,如果没有其他(以前未阐明的)假设,通常是不正确的。我们通过反例证明,原始的自由能引理以表面上的价值为单位是错误的。我们进一步表明,这种自由能引理在坚持下,意味着变异密度和千古的条件密度的平等。基于贝叶斯推论的解释取决于这一点,因此我们得出的结论是没有足够的合理性。此外,我们强调说,在自由能原理和引理的较新的制剂中呈现的变异密度与较旧的作品不同的变量进行了参数,从而导致对理论的解释实质上不同。请注意,我们只会在讨论的出版物中强调一些特定的问题。这些问题并不能最终排除,自由能原理背后的一般思想值得追求。
We summarize the original formulation of the free energy principle, and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for and reveal, up to now unacknowledged, differences to newer formulations of the free energy principle. In particular, we reveal that various definitions of the "Markov blanket" proposed in different works are not equivalent. We show that crucial steps in the free energy argument which involve rewriting the equations of motion of systems with Markov blankets, are not generally correct without additional (previously unstated) assumptions. We prove by counterexample that the original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma, when it does hold, implies equality of variational density and ergodic conditional density. The interpretation in terms of Bayesian inference hinges on this point, and we hence conclude that it is not sufficiently justified. Additionally, we highlight that the variational densities presented in newer formulations of the free energy principle and lemma are parameterised by different variables than in older works, leading to a substantially different interpretation of the theory. Note that we only highlight some specific problems in the discussed publications. These problems do not rule out conclusively that the general ideas behind the free energy principle are worth pursuing.