Brain Awareness Week at the European Parliament

How our brain works:Recent advances in the theory of brain function

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“Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism” - Hermann Ludwig Ferdinand von Helmholtz

Thomas Bayes

Geoffrey Hinton

Richard Feynman

From the Helmholtz machine to the Bayesian brain and self-

organization

Hermann Haken2

tem

pera

ture

What is the difference between a snowflake and a bird?

Phase-boundary

…a bird can avoid surprises

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What is the difference between snowfall and a flock of birds?

Ensemble dynamics and swarming

…birds (biological agents) stay in the same place

They resist the second law of thermodynamics, which says that their entropy should increase

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This means biological agents must self-organize to minimise surprise. In other words, to ensure they occupy a limited number of (attracting) states

0

( ) ( ) ln ( | )H S ST

dt t t p s m

But what is the entropy?

A

s

…entropy is just average surprise

Low surprise (I am usually here) High surprise (I am never here)

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But there is a small problem… agents cannot measure their surprise

But they can measure their free-energy, which is always bigger than surprise

This means agents should minimize their free-energy. So what does this mean?

?

( ) ( )t tF S

s

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What is free-energy?

…free-energy is basically prediction error

where small errors mean low surprise

sensations – predictions

= prediction error

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How can we minimize prediction error (free-energy)?

Change sensory input

sensations – predictions

Prediction error

Change predictions

Action Perception

…prediction errors drive action and perception to suppress themselves8

Models (hypotheses)Models (hypotheses)

Prediction error

Sensory input

But where do predictions come from?

…they come from the brain’s model of the world

This means the brain models and predicts its sensations (cf, a Helmholtz machine).

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Adjust hypotheses

sensory input

Backward connections return predictions

…by hierarchical message passing in the brain

prediction

Forward connections convey feedback

So how do prediction errors change predictions?

Prediction errors

Predictions

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Why hierarchical message passing?

…because the brain is organized hierarchically, where each level predicts the level below

cortical layers

Specialised cortical areas

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Backward predictions

Forward prediction error

( )i x

( )i x

( )i v

( 1)i v

( )s t

( )i v( 1)i x

( 1)i x

( 1)i v

( 2)i v

David Mumford

Hierarchical message passing in the brain

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predictions

Reflexes to action

a

action

( )s a

dorsal root

ventral horn

sensory error

What about action?

Action can only suppress (sensory) prediction error. This means action fulfils our (sensory) predictions 13

Summary

•Biological agents resist the second law of thermodynamics

•They must minimize their average surprise (entropy)

•They minimize surprise by suppressing prediction error (free-energy)

•Prediction error can be reduced by changing predictions (perception)

•Prediction error can be reduced by changing sensations (action)

•Perception entails recurrent message passing in the brain to optimise predictions

•Action makes predictions come true (and minimises surprise)

Examples:

Perception (birdsongs)

Action (goal-directed reaching)

Policies (the mountain car problem)

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Making bird songs with Lorenz attractors

SyrinxVocal centre

1

2

vv

v

time (sec)

Fre

qu

en

cy

Sonogram

0.5 1 1.5causal states

hidden states

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x

x

v( )s t

v

10 20 30 40 50 60-5

0

5

10

15

20prediction and error

10 20 30 40 50 60-5

0

5

10

15

20hidden states

Backward predictions

Forward prediction error

10 20 30 40 50 60-10

-5

0

5

10

15

20

causal states

Perception and message passing

stimulus

0.2 0.4 0.6 0.82000

2500

3000

3500

4000

4500

5000

time (seconds)

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Perceptual categorization

Freq

uenc

y (H

z) Song a

time (seconds)

Song b Song c

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Hierarchical models of birdsong: sequences of sequences

SyrinxNeuronal hierarchy

Time (sec)

Fre

qu

en

cy (

KH

z)

sonogram

0.5 1 1.5

(1)1(1)2

v

v

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Fre

quen

cy (

Hz)

percept

Fre

quen

cy (

Hz)

no top-down messages

time (seconds)

Fre

quen

cy (

Hz)

no lateral messages

0.5 1 1.5

-40

-20

0

20

40

60

LFP

(m

icro

-vol

ts)

LFP

-60

-40

-20

0

20

40

60

LFP

(m

icro

-vol

ts)

LFP

0 500 1000 1500 2000-60

-40

-20

0

20

40

60

peristimulus time (ms)

LFP

(m

icro

-vol

ts)

LFP

Simulated lesions and hallucinations

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a

Vs w

J

1

2

xs w

x

(1)v (1)x

(1)v

(1)v

1J

1x

2x2J

(0,0)

1 2 3( , , )V v v v

(2)v(1)x

Descending sensory prediction

error

visual input

proprioceptive input

Action, predictions and priors

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18( ) x

xx

a xx

f

True equations of motion

-2 -1 0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

position

( )x

heig

ht

The mountain car problem

position happiness

The cost-function

x

xxf

cxx

Policy (predicted motion)

( , )c x h

( )h( )x

The environment

Adriaan Fokker Max Planck

“I expect to move faster when cost is positive” 21

With cost (i.e., exploratory

dynamics)

Exploring & exploiting the environment

a

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Using just the free-energy principle and a simple gradient ascent scheme, we have solved a benchmark problem in optimal control theory using a handful of learning trials.

Policies and prior expectations

If priors are so important, where do they come from?

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The selection of adaptive predictions

Darwinian evolution of virtual block creatures. A population of several hundred creatures is created within a supercomputer, and each creature is tested for their ability to perform a given task, such the ability to swim in a simulated water environment. The successful survive, and their virtual genes are copied, combined, and mutated to make offspring. The new creatures are again tested, and some may be improvements on their parents. As this cycle of variation and selection continues, creatures with more and more successful behaviours can emerge.

…we inherit them

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310 s

010 s

310 s

610 s

1510 s

Perception and Action: The optimisation of neuronal and neuromuscular activity to suppress prediction errors (or free-energy) based on generative models of sensory data.

Learning and attention: The optimisation of synaptic gain and efficacy over seconds to hours, to encode the precisions of prediction errors and causal structure in the sensorium. This entails suppression of free-energy over time.

Neurodevelopment: Model optimisation through activity-dependent pruning and maintenance of neuronal connections that are specified epigenetically

Evolution: Optimisation of the average free-energy (free-fitness) over time and individuals of a given class (e.g., conspecifics) by selective pressure on the epigenetic specification of their generative models.

Time-scale Free-energy minimisation leading to…

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Thank you

And thanks to collaborators:

Jean DaunizeauLee HarrisonStefan KiebelJames Kilner

Klaas Stephan

And colleagues:

Peter DayanJörn DiedrichsenPaul Verschure

Florentin Wörgötter

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