
Free energy principle - flying_sheep
https://en.wikipedia.org/wiki/Free_energy_principle
======
rotskoff
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.

~~~
Koshkin
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.

------
hnarayanan
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...](http://iopscience.iop.org/article/10.1088/0953-8984/22/19/194122/meta)

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

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

------
lucb1e
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.

~~~
progval
> 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.

~~~
tzs
> "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.

~~~
progval
Both are the same thing (kind of)

------
irickt
Recent discussion about a tutorial and software:
[https://news.ycombinator.com/item?id=17474949](https://news.ycombinator.com/item?id=17474949)

------
Sharlin
SSC on Friston and the free energy principle:
[http://slatestarcodex.com/2018/03/04/god-help-us-lets-try-
to...](http://slatestarcodex.com/2018/03/04/god-help-us-lets-try-to-
understand-friston-on-free-energy/)

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

------
uberstuber
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/](https://www.ribbonfarm.com/2018/04/06/deep-laziness/)

------
amthewiz
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.

------
madhadron
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.

