I have yet to see any concrete algorithmic claim about the brain that was not more easily and intuitively [from my perspective] discussed without mentioning FEP.
There is a claim about a brain, but a neural organoid: “We develop DishBrain, a system that harnesses the inherent adaptive computation of neurons in a structured environment. In vitro neural networks from human or rodent origins are integrated with in silico computing via a high-density multielectrode array. Through electrophysiological stimulation and recording, cultures are embedded in a simulated game-world, mimicking the arcade game “Pong.” Applying implications from the theory of active inference via the free energy principle, we find apparent learning within five minutes of real-time gameplay not observed in control conditions. Further experiments demonstrate the importance of closed-loop structured feedback in eliciting learning over time. Cultures display the ability to self-organize activity in a goal-directed manner in response to sparse sensory information about the consequences of their actions, which we term synthetic biological intelligence.” (Kagan et al., Oct 2022). It’s arguably hard (unless you can demonstrate that it’s easy) to make sense of the DishBrain experiment not through the FEP/Active Inference lens, even though it should be possible, as you rightly highlighted: the FEP is a mathematical tool that should help to make sense of the world (i.e., doing physics), by providing a principled way of doing physics on the level of beliefs, a.k.a. Bayesian mechanics (Ramstead et al., Feb 2023).
It’s interesting that you mention Noether’s theorem, because in the “Bayesian mechanics” paper, the authors use it as the example as well, essentially repeating something very close to what you have said in section 1:
To sum up: principles like the FEP, the CMEP, Noether’s theorem, and the principle of stationary action are mathematical structures that we can use to develop mechanical theories (which are also mathematical structures) that model the dynamics of various classes of physical systems (which are also mathematical structures). That is, we use them to derive the mechanics of a system (a set of equations of motion); which, in turn, are used to derive or explain dynamics. A principle is thus a piece of mathematical reasoning, which can be developed into a method; that is, it can applied methodically—and more or less fruitfully—to specific situations. Scientists use these principles to provide an interpretation of these mechanical theories. If mechanics explain what a system is doing, in terms of systems of equations of movement, principles explain why. From there, scientists leverage mechanical theories for specific applications. In most practical applications (e.g., in experimental settings), they are used to make sense of a specific set of empirical phenomena (in particular, to explain empirically what we have called their dynamics). And when so applied, mechanical theories become empirical theories in the ordinary sense: specific aspects of the formalism (e.g., the parameters and updates of some model) are systematically related to some target empirical phenomena of interest. So, mechanical theories can be subjected to experimental verification by giving the components specific empirical interpretation. Real experimental verification of theories, in turn, is more about evaluating the evidence that some data set provides for some models, than it is about falsifying any specific model per se. Moreover, the fact that the mechanical theories and principles of physics can be used to say something interesting about real physical systems at all—indeed, the striking empirical fact that all physical systems appear to conform to the mechanical theories derived from these principles; see, e.g., [81]—is distinct from the mathematical “truth” (i.e., consistency) of these principles.
Note that the FEP theory has developed significantly only in the last year or so: apart from these two references above, the shift to the path-tracking (a.k.a. path integral) formulation of the FEP (Friston et al., Nov 2022) for systems without NESS (non-equilibrium steady state) has been significant. So, judging the FEP on pre-2022 work may not do it justice.
There is a claim about a brain, but a neural organoid: “We develop DishBrain, a system that harnesses the inherent adaptive computation of neurons in a structured environment. In vitro neural networks from human or rodent origins are integrated with in silico computing via a high-density multielectrode array. Through electrophysiological stimulation and recording, cultures are embedded in a simulated game-world, mimicking the arcade game “Pong.” Applying implications from the theory of active inference via the free energy principle, we find apparent learning within five minutes of real-time gameplay not observed in control conditions. Further experiments demonstrate the importance of closed-loop structured feedback in eliciting learning over time. Cultures display the ability to self-organize activity in a goal-directed manner in response to sparse sensory information about the consequences of their actions, which we term synthetic biological intelligence.” (Kagan et al., Oct 2022). It’s arguably hard (unless you can demonstrate that it’s easy) to make sense of the DishBrain experiment not through the FEP/Active Inference lens, even though it should be possible, as you rightly highlighted: the FEP is a mathematical tool that should help to make sense of the world (i.e., doing physics), by providing a principled way of doing physics on the level of beliefs, a.k.a. Bayesian mechanics (Ramstead et al., Feb 2023).
It’s interesting that you mention Noether’s theorem, because in the “Bayesian mechanics” paper, the authors use it as the example as well, essentially repeating something very close to what you have said in section 1:
Note that the FEP theory has developed significantly only in the last year or so: apart from these two references above, the shift to the path-tracking (a.k.a. path integral) formulation of the FEP (Friston et al., Nov 2022) for systems without NESS (non-equilibrium steady state) has been significant. So, judging the FEP on pre-2022 work may not do it justice.