brain awareness week at the european parliament
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Brain Awareness Week at the European Parliament. How our brain works: Recent advances in the theory of brain function. - PowerPoint PPT PresentationTRANSCRIPT
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
4
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)
Freq
uenc
y
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)
Freq
uenc
y (K
Hz)
sonogram
0.5 1 1.5
(1)1(1)2
vv
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Freq
uenc
y (H
z)
percept
Freq
uenc
y (H
z)no top-down messages
time (seconds)
Freq
uenc
y (H
z)
no lateral messages
0.5 1 1.5
-40
-20
0
20
40
60
LFP
(mic
ro-v
olts
)
LFP
-60
-40
-20
0
20
40
60
LFP
(mic
ro-v
olts
)
LFP
0 500 1000 1500 2000-60
-40
-20
0
20
40
60
peristimulus time (ms)
LFP
(mic
ro-v
olts
)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
xxa 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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