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Free energy principle (wikipedia.org)
79 points by flying_sheep 8 months ago | hide | past | web | favorite | 19 comments

I'm seeing a lot of misinformation / misunderstanding in the comments. My PhD was primarily about nonequilibrium statistical physics, so let me try to give a simple explanation of free energy and its relevance for biological systems.

1. The free energy is a concept from _equilibrium_ statistical physics. Most simply, it accounts for a balance between minimizing energy (what systems do at low temperature) and maximizing entropy (when systems become disordered, as happens at high temperatures). The interesting regime is at temperatures where the energetic and entropic contributions are both important.

2. In biology / biophysics, this is a heavily used concept. For example, the most likely configuration of a protein (that is, the arrangement of the atoms in the molecule) minimizes the free energy. Of course, there are fluctuations, and the "free energy surface" can have multiple minima, corresponding to different states. This is an approximation that usually works because on small scales, the environment of a protein can often be equilibrium like.

3. The idea that a biological systems maintain a nonequilibrium steady state (all living systems are out of equilibrium) by minimizing a free energy functional is kind of like the hidden variables hypothesis in quantum mechanics. Basically, the conjecture described in the articles is that there's some unknown free energy that you can write down (similar to a graphical model with hidden variables) that the cell is trying to minimize.

4. It should be emphasized that this perspective is attempting to map a nonequilibrium system onto an equilibrium system and there are many cases where such a correspondence is impossible (formally all equilibrium systems have a probability distribution called a boltzmann distribution and some nonequilibrium systems have statistics that simply cannot be captured by such a distribution).

5. To editorialize, because nonequilibrium steady states are fundamentally dynamical, I would not be willing to endorse this view. Ultimately, this "principle" asserts that there is some non-dynamical state function for the dynamical systems encountered in biology.

Well, to be fair, Friston's use of the term "free energy" has little to do with its use in thermodynamics (and, consequently, in biology). Here it is used to denote something to be minimized using the methods of "variational Bayesian inference" as a way of explaining phenomena studied by cognitive science in general and in the subject of machine learning in particular.

Not completely sure why this is on HN, but I am happy to see it on here! :) A good chunk of my PhD (many years ago) relied on the minimisation of free energy to understand the evolution of biological systems. e.g. Studying the growth of tumours: http://iopscience.iop.org/article/10.1088/0953-8984/22/19/19...

This has prompted me to go take a look at the state of the art.

You seem eminently well qualified to give us a ELI5 here. How about it? (The other ELI5 here didn't do it for me.)

> why this is on HN

Because [0]

> machine learning

> Bayesian

[0] https://en.m.wikipedia.org/wiki/Variational_Bayesian_methods

I don't even understand the first paragraph, e.g. what's the 'order' which 'the biological system' is trying to maintain? And what's a 'free energy functional'? Can someone ELI5 what this article is about? The title sounded like a perpetuum mobile, but that doesn't seem to be it.

> what's the 'order' which 'the biological system' is trying to maintain?

Being stable, ie. not entering a cascade of events that leads to death.

> And what's a 'free energy functional'?

"free energy functional of their internal states" means the free energy, computed as a function from their internal state. ie. each internal state has a corresponding internal energy.

> The title sounded like a perpetuum mobile, but that doesn't seem to be it.

Actually, it is. It's just a very very complex mobile. With some energy input (drinking, photosynthesis, ...) and some energy output (heat, sweat, ...)

> Can someone ELI5 what this article is about?

I'm going to try, but I'm no biologist or chemist so I can't certify this is correct.

Living beings are very complex systems, which could easily enter a bad state, which would lead to a worse state, etc until death.

To prevent that, they restrict themselves to some "good" states, which have little "free energy". The thing with "free energy" is that it cannot increase easily, so the beings cannot enter a state with higher "free energy" than they currently have.

If all possible bad states have higher "free energy" than the current state, then they cannot reach it, which is good.

>Living beings are very complex systems, which could easily enter a bad state, which would lead to a worse state, etc until death.

I'm still equally confused as OP, right at this initial building block.

A state is just a collection of atoms in a certain configuration. Some states make up a living creature. Some others make up a dead creature. Most creatures want to avoid transitioning from an alive state to a dead state. Most of the time you would say that most creatures want to avoid dying, but because of the ideas that come next it is important to start talking in terms of states.

> "free energy functional of their internal states" means the free energy, computed as a function from their internal state. ie. each internal state has a corresponding internal energy.

I think what is confusing people (it is certainly confusing me) is the distinction between a function and a functional.

Both are the same thing (kind of)

The name “functional” is commonly used to refer to a function which takes a whole function (rather than, say, a number) as input. A simple example of a functional is the definite integral (area under the curve) over an interval.

Think about an atom bomb. Large amount of energy is released in a small space. This energy is always there but we don't see huge explosions everywhere.

Recent discussion about a tutorial and software: https://news.ycombinator.com/item?id=17474949

SSC on Friston and the free energy principle: http://slatestarcodex.com/2018/03/04/god-help-us-lets-try-to...

The consensus seems to be that there could be something to it but darn Friston doesn’t make it easy for others to understand.

Here's a ribbonfarm article on using this sort of natural laziness to build things (architecture, behaviors, systems): https://www.ribbonfarm.com/2018/04/06/deep-laziness/

As I understand, the basic idea is to minimize surprise over the organism’s life using models of the world to predict the causes behind what the organism observes and actions to keep the organism within states suitable for survival.

tl;dr: Things look profound when you use the wrong mathematical language and name arbitrary expressions in your math with the same words as other scientists use to summarize their observations. Don't waste your time, though.

When I transitioned from physics to biology, I was really interested in this kind of work. All the papers trying to do so, aside from one, did not pan out on closer investigation. That one was a model of branching fluid transport networks that noted that most such networks had the same number of branch levels, and gave an interesting calculation of fluid flow resistance to show that was an optimum. The only optimizing framework that gives you any mileage in a general way in biology is evolutionary game theory.

I spent a few minutes poking around this. The framework is straightforward once you pull all the verbiage off of it.

Consider usual statistical inference in the language of game theory. It's a two player game (nature and the actor making a decision). First nature makes a move (choosing a state of nature), and then the actor makes a move (the decision or inference) given limited information on nature's move. Since nature's move doesn't depend on the actor's move, you can optimize the actor's strategy given nature's strategy without having to worry about Nash equilibria.

This extends the framework to a repeated game. At each stage the actor takes an action and nature takes an action. The actor's move changes what partial information it gets from nature's move. Nature's moves continue not to depend on the actor's move.

Now, in general in inference you need some additional principle to choose from the many strategies that are each optimal in somewhat different ways. Friston assumes that all the actors involved are Bayesian.

Once he's assumed that, he has a well defined framework for optimizing the player's behavior. It turns out that doing these calculations directly is intractable, but the risk he's actually minimizing is bounded by an expression that looks like free energy in statistical mechanics, so he minimizes that instead.

Now, there are some problems there:

1. It assumes that actors are Bayesian. That's not true in general. In the 1960's and 1970's a set of theorems pointed to rational actors being Bayesian, but as the field matured it turned out that the general case wasn't true. It only worked in the very restricted case where it was discovered. It's common that people outside of statistics only know the early excitement and not the later disappointment, though, so this keeps coming up.

2. The framework was developed assuming that the world doesn't act in response to the actor. You could kludge that in, but it's exactly that: a kludge. If you don't have other actors, then you don't really need internal state. You just need a search strategy.

3. The framework is too general. You can extract almost anything you want by putting in the right functions for its various terms.

4. In the papers I looked at this morning, various parts of the math are named with words taken from problem domains, but those words are not operationalized. Without that, there's no reason to think any of this is relevant to reality.

Biology isn't physics. Dragging universal extremum principles in doesn't yield much in biology. (And has probably painted physicists into several corners at this point, too.) If you're interested in neurobiology, go look at actual organisms and their dynamics.

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