对自由能原理某些部分的技术批判
A Technical Critique of Some Parts of the Free Energy Principle
摘要：
我们总结了自由能原理的原始表述，并强调了一些技术问题。我们讨论这些问题如何影响相关的结果，涉及广义坐标，并在适当的情况下，提到后果，并揭示，到目前为止未被承认的，新配方的自由能原理的差异。特别是，我们发现，各种定义的“马尔可夫毯”提出了不同的作品是不等价的。我们表明，在自由能参数的关键步骤，涉及重写系统的运动方程与马尔可夫毯，一般是不正确的，没有额外的（以前未说明）的假设。我们证明了反例，原来的自由能引理，当采取的面值，是错误的。我们进一步表明，这个自由能引理，当它成立时，意味着平等的变分密度和遍历条件密度。贝叶斯推断的解释取决于这一点，因此我们得出结论，它是不充分的理由。此外，我们强调，在新的配方的自由能原理和引理的变分密度参数化不同的变量比在旧的作品，导致一个实质上不同的解释理论。请注意，我们在讨论的出版物中只强调了一些特定的问题。这些问题并不能最终排除自由能原理背后的一般思想是值得追求的。
英文摘要：
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.
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