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An introduction to free energy

Stephen Francis Mann stephenfmann@gmail.com

Max Planck Institute for Evolutionary Anthropology

These slides: stephenfmann.com/links/sfm20221008

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Principles can be normative or descriptive (or both!)

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Sand

Water

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Sand

Water

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Sand

Water

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Sand

Water

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Sand

Water

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Air

Glass

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Air

Glass

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Air

Glass

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Air

Glass

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Air

Glass

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

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Sand

Water

Path ← argmin Time(path)

“Choose the path that takes the shortest time”

Weights ← argmin Error(weights)

“Choose the weights that give the smallest error”

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Really simple models of the

free energy principle

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2.1 Inference

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Meow!

Purr…

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Meow!

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Bogacz (2017)

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x = w²

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Bogacz (2017)

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x = N(x; w², Σ_x)

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Bogacz (2017)

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x = N(x; w², Σ_x)

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Bogacz (2017)

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x = N(x; w², Σ_x)

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Bogacz (2017)

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Bogacz (2017)

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Bogacz (2017)

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Really simple models of the

free energy principle

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2.2 Action

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Meow!

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Really simple models of the

free energy principle

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2.3 Selection

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Parr et al (2022:7, Fig. 1.2)

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Really simple models of the

free energy principle

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2.4 Extensions

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W₂

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W₂

W₃

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W₂

W₃

W₄

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W₂

W₃

X₂

W₄

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W₂

W₃

X₂

Z₂

W₄

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W₂

W₃

X₂

Z₂

W₄

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Outstanding issues

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Issue 1

It’s not free energy: it’s surprisal.

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The motivation for positing variational inference is not yet strong, but many people assert that it is mathematically proven.

Their arguments are not convincing – sometimes they are not even coherent.

They point to computational intractability – but these organisms are not literally performing computations, they are just “entailing” distributions.

If you can “entail” minimising free energy then you can “entail” minimising surprise directly. Computational intractability doesn’t come into it, because there is no actual computation taking place.

If we can be instrumentalists about HOW the thing is minimising surprise, then why are we demanding that it MUST be using variational inference (as opposed to some other imaginary mechanism)?

In other words: instrumentalist posits are very cheap. Why don't we posit direct surprise minimisation or exact Bayesian inference?

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Issue 1

It’s not free energy: it’s surprisal.

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F

bit.ly/sfm20221008

The motivation for positing variational inference is not yet strong, but many people assert that it is mathematically proven.

Their arguments are not convincing – sometimes they are not even coherent.

They point to computational intractability – but these organisms are not literally performing computations, they are just “entailing” distributions.

If you can “entail” minimising free energy then you can “entail” minimising surprise directly. Computational intractability doesn’t come into it, because there is no actual computation taking place.

If we can be instrumentalists about HOW the thing is minimising surprise, then why are we demanding that it MUST be using variational inference (as opposed to some other imaginary mechanism)?

In other words: instrumentalist posits are very cheap. Why don't we posit direct surprise minimisation or exact Bayesian inference?

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Issue 1

It’s not free energy: it’s surprisal.

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F

bit.ly/sfm20221008

The motivation for positing variational inference is not yet strong, but many people assert that it is mathematically proven.

Their arguments are not convincing – sometimes they are not even coherent.

They point to computational intractability – but these organisms are not literally performing computations, they are just “entailing” distributions.

If you can “entail” minimising free energy then you can “entail” minimising surprise directly. Computational intractability doesn’t come into it, because there is no actual computation taking place.

If we can be instrumentalists about HOW the thing is minimising surprise, then why are we demanding that it MUST be using variational inference (as opposed to some other imaginary mechanism)?

In other words: instrumentalist posits are very cheap. Why don't we posit direct surprise minimisation or exact Bayesian inference?

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Issue 1

It’s not free energy: it’s surprisal.

The argument that

Everything is trying to minimise surprisal

therefore

Everything minimises free energy

needs another premise.

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The motivation for positing variational inference is not yet strong, but many people assert that it is mathematically proven.

Their arguments are not convincing – sometimes they are not even coherent.

They point to computational intractability – but these organisms are not literally performing computations, they are just “entailing” distributions.

If you can “entail” minimising free energy then you can “entail” minimising surprise directly. Computational intractability doesn’t come into it, because there is no actual computation taking place.

If we can be instrumentalists about HOW the thing is minimising surprise, then why are we demanding that it MUST be using variational inference (as opposed to some other imaginary mechanism)?

In other words: instrumentalist posits are very cheap. Why don't we posit direct surprise minimisation or exact Bayesian inference?

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Issue 2

It’s not surprisal: it’s probability.

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Issue 2

It’s not surprisal: it’s probability.

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Issue 2

It’s not surprisal: it’s probability.

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Issue 2

It’s not surprisal: it’s probability.

Things that survive long enough will tend to be found in states conducive to their survival

This is a restatement of natural selection.

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Define probability w.r.t past success

Everything tries to maximise probability

Everything tries to minimise surprise

Everything tries to minimise free energy

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Define probability w.r.t past success

Everything tries to maximise probability

Everything tries to minimise surprise

Everything tries to minimise free energy

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Natural selection

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Define probability w.r.t past success

Everything tries to maximise probability

Everything tries to minimise surprise

Everything tries to minimise free energy

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Natural selection

By definition!

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Define probability w.r.t past success

Everything tries to maximise probability

Everything tries to minimise surprise

Everything tries to minimise free energy

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Natural selection

By definition!

Why not minimise surprise directly?

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Define probability w.r.t past success

Everything tries to maximise probability

Everything tries to minimise surprise

Everything tries to minimise free energy

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Natural selection

By definition!

Why not minimise surprise directly?

Why not some other approximation?

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Issue 3

The interpretation of p(w,x) is unorthodox.

Both probabilities and preferences simultaneously?

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Issue 4

Realism vs instrumentalism.

Proponents tend to pick and choose depending on the case at hand.

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Parr et al (2022:7, Fig. 1.2)

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Parr et al (2022:7, Fig. 1.2)

Natural selection
Probabilities = preferences
Instrumentalism

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Parr et al (2022:7, Fig. 1.2)

Natural selection
Probabilities = preferences
Instrumentalism

Variational inference
Probabilities =?= preferences
Realism

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References

Bogacz, R. (2017). A tutorial on the free-energy framework for modelling perception and learning. Journal of Mathematical Psychology, 76, 198–211. https://doi.org/10.1016/j.jmp.2015.11.003

Mann, S. F., Pain, R., & Kirchhoff, M. D. (2022). Free Energy: A User’s Guide. Biology & Philosophy, 37(4), 35. https://doi.org/10.1007/s10539-022-09864-z

Parr, T., Pezzulo, G., & Friston, K. J. (2022). Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. MIT Press.

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Active inference and the self

Allen, M., & Friston, K. J. (2018). From cognitivism to autopoiesis: Towards a computational framework for the embodied mind. Synthese, 195(6), 2459–2482. https://doi.org/10.1007/s11229-016-1288-5

Deane, G. (2020). Dissolving the self: Active inference, psychedelics, and ego-dissolution. Philosophy and the Mind Sciences, 1(I), Article I. https://doi.org/10.33735/phimisci.2020.I.39

Limanowski, J., & Friston, K. (2020). Attenuating oneself: An active inference perspective on “selfless” experiences. Philosophy and the Mind Sciences, 1(I), Article I. https://doi.org/10.33735/phimisci.2020.I.35

Seth, A. K., & Friston, K. J. (2016). Active interoceptive inference and the emotional brain. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1708), 20160007. https://doi.org/10.1098/rstb.2016.0007

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