You can show that, in order for an agent to persist, it needs to have the capacity to observe and learn about its environment. The math is a more complex than I want to get into here...
Do you have a citation for this? I went looking for the supposed math behind that claim a couple years back, and found one section of one Friston paper which had an example system which did not obviously generalize particularly well, and also used a kinda-hand-wavy notion of “Markov blanket” that didn’t make it clear what precisely was being conditioned on (a critique which I would extend to all of the examples you list). And that was it; hundreds of excited citations chained back to that one spot. If anybody’s written an actual explanation and/or proof somewhere, that would be great.
So, let me give you the high level intuitive argument first, where each step is hopefully intuitively obvious:
The environment contains variance. Sometimes it’s warmer, sometimes it’s colder. Sometimes it is full of glucose, sometimes it’s full of salt.
There exist only a subset of states which an agent can persist in. Obviously the stuff the agent is made out of will persist but the agent itself (as a pattern of information) will dissipate into the environment if it doesn’t exist in those states.
Therefore, the agent needs to be able to observe its surroundings and take action in order to steer into the parts of state-space where it will persist. Even if the system is purely reactive it must act-as-if it is doing inference, because there is variance in the time lag between receiving an observation and when you need to act on it. (Another way to say this is that an agent must be a control system that contends with temporal lag).
The environment is also constantly changing. So even if the agent is magically gifted with the ability to navigate into states via observation and action to begin with, whatever model it is using will become out of date. Then its steering will become wrong. Then it dies.
There is another approach to persistence (become a very hard rock) but that involves stopping being an agent. Being hard means committing very so hard to a single pattern that you can’t change. That does mean, good news, the environment can’t change you. Bad news, you can’t change yourself either, and a minimal amount of self-change is required in order to take action (actions are always motions!).
I, personally, find this quite convincing. I’m curious what about it doesn’t seem simply intuitively obvious. I agree that having formal mathematical proof is valuable and good, but this point seems so clear to me that I feel quite comfortable with assuming it even without.
Some papers that are related, not sure which you were referring to. I think they lay it out in sufficient detail that I’m convinced but if you think there’s a mistake or gap I’d be curious to hear about it.
It seems pretty obvious to me that if (1) if a species of bacteria lives in an extremely uniform / homogeneous / stable external environment, it will eventually evolve to not have any machinery capable of observing and learning about its external environment; (2) such a bacterium would still be doing lots of complex homeostasis stuff, reproduction, etc., such that it would be pretty weird to say that these bacteria have fallen outside the scope of Active Inference theory. (I.e., my impression was that the foundational assumptions / axioms of Free Energy Principle / Active Inference were basically just homeostasis and bodily integrity, and this hypothetical bacterium would still have both of those things.) (Disclosure: I’m an Active Inference skeptic.)
This paper and this one are to my knowledge the most recent technical expositions of the FEP. I don’t know of any clear derivations of the same in the discrete setting.
Do you have a citation for this? I went looking for the supposed math behind that claim a couple years back, and found one section of one Friston paper which had an example system which did not obviously generalize particularly well, and also used a kinda-hand-wavy notion of “Markov blanket” that didn’t make it clear what precisely was being conditioned on (a critique which I would extend to all of the examples you list). And that was it; hundreds of excited citations chained back to that one spot. If anybody’s written an actual explanation and/or proof somewhere, that would be great.
So, let me give you the high level intuitive argument first, where each step is hopefully intuitively obvious:
The environment contains variance. Sometimes it’s warmer, sometimes it’s colder. Sometimes it is full of glucose, sometimes it’s full of salt.
There exist only a subset of states which an agent can persist in. Obviously the stuff the agent is made out of will persist but the agent itself (as a pattern of information) will dissipate into the environment if it doesn’t exist in those states.
Therefore, the agent needs to be able to observe its surroundings and take action in order to steer into the parts of state-space where it will persist. Even if the system is purely reactive it must act-as-if it is doing inference, because there is variance in the time lag between receiving an observation and when you need to act on it. (Another way to say this is that an agent must be a control system that contends with temporal lag).
The environment is also constantly changing. So even if the agent is magically gifted with the ability to navigate into states via observation and action to begin with, whatever model it is using will become out of date. Then its steering will become wrong. Then it dies.
There is another approach to persistence (become a very hard rock) but that involves stopping being an agent. Being hard means committing very so hard to a single pattern that you can’t change. That does mean, good news, the environment can’t change you. Bad news, you can’t change yourself either, and a minimal amount of self-change is required in order to take action (actions are always motions!).
I, personally, find this quite convincing. I’m curious what about it doesn’t seem simply intuitively obvious. I agree that having formal mathematical proof is valuable and good, but this point seems so clear to me that I feel quite comfortable with assuming it even without.
Some papers that are related, not sure which you were referring to. I think they lay it out in sufficient detail that I’m convinced but if you think there’s a mistake or gap I’d be curious to hear about it.
The free energy principle made simpler but not too simple—a more formal take
A free energy principle for a particular physics—the most formal take I’m aware of
It seems pretty obvious to me that if (1) if a species of bacteria lives in an extremely uniform / homogeneous / stable external environment, it will eventually evolve to not have any machinery capable of observing and learning about its external environment; (2) such a bacterium would still be doing lots of complex homeostasis stuff, reproduction, etc., such that it would be pretty weird to say that these bacteria have fallen outside the scope of Active Inference theory. (I.e., my impression was that the foundational assumptions / axioms of Free Energy Principle / Active Inference were basically just homeostasis and bodily integrity, and this hypothetical bacterium would still have both of those things.) (Disclosure: I’m an Active Inference skeptic.)
This paper and this one are to my knowledge the most recent technical expositions of the FEP. I don’t know of any clear derivations of the same in the discrete setting.
You might want to look here or here.