Abstract Predictive coding models and the free-energy principle, suggests that cortical activity in sensory brain areas reflects the precision of prediction errors and not just the sensory evidence or prediction errors per se. If we assume that neuronal activity encodes a probabilistic representation of the world that optimizes free-energy in a Bayesian fashion, then, because free-energy bounds surprise or the (negative) log-evidence for internal models of the world, this optimization can be regarded as evidence accumulation or (generalized) predictive coding. Crucially, both predictions about the state of the world generating sensory data and the precision of those data have to be optimized. In other words, we have to make predictions (test hypotheses) about the content of the sensorium and predict our confidence in those hypotheses. I hope to demonstrate the meta-representational aspect of inference using simulations of visual searches and action selection - to illustrate their nature and promote discussion about its role in high-order cognition. November 29th 4:30 – 6:00pm Old Library Karl Friston Meta-cognition, prediction, precision (Discussant, Andreas Roepstorff, Aarhus) SEMINARS ON META-COGNITION, 2012–2013
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Abstract Predictive coding models and the free-energy principle, suggests that cortical activity in sensory brain areas reflects the precision of prediction.
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Abstract
Predictive coding models and the free-energy principle, suggests that cortical activity in sensory brain areas reflects the precision of prediction errors and not just the sensory evidence or prediction errors per se. If we assume that neuronal activity encodes a probabilistic representation of the world that optimizes free-energy in a Bayesian fashion, then, because free-energy bounds surprise or the (negative) log-evidence for internal models of the world, this optimization can be regarded as evidence accumulation or (generalized) predictive coding. Crucially, both predictions about the state of the world generating sensory data and the precision of those data have to be optimized. In other words, we have to make predictions (test hypotheses) about the content of the sensorium and predict our confidence in those hypotheses. I hope to demonstrate the meta-representational aspect of inference using simulations of visual searches and action selection - to illustrate their nature and promote discussion about its role in high-order cognition.
November 29th 4:30 – 6:00pm Old LibraryKarl Friston
Meta-cognition, prediction, precision (Discussant, Andreas Roepstorff, Aarhus)
SEMINARS ON META-COGNITION, 2012–2013
The basic idea: active inference and free energy
Beliefs about beliefs: beliefs about uncertainty
Beliefs about beliefs: beliefs about precision and agency
“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” - von Helmholtz
Thomas Bayes
Geoffrey Hinton
Richard Feynman
From the Helmholtz machine to the Bayesian brain and self-organization
Hermann Haken
Richard GregoryHermann von Helmholtz
tem
pera
ture
What is the difference between a snowflake and a bird?
Phase-boundary
…a bird can act (to avoid surprises)
( , ) ss a g ψ ω
Hidden states in the world Internal states of the agentSensations
argmin ( , )F s
argmin ( , )a F s μ a
( , ) xa ψ f ψ ω
ω
Action
External states
FluctuationsPosterior expectations
The basic ingredients
What we need to explain: how do we minimise the dispersion of sensory states (homoeostasis)?
ln ( ( ) | ) [ ( | )]p s t m dt H p s m
( , , ) ln ( | ) [ ( | ), ( | )]
[ ln ( , )] [ ( | )]
KL
q
F s m p s m D q p s
E p s H q
( ) ln ( ( ) | ) [ ( | )]dtF t dt p s t m H p s m
The principle of least action
The principle of least free energy (minimising surprise)
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 optimize predictions
Action makes predictions come true (and minimizes surprise)
Beliefs about beliefs: beliefs about uncertainty
Perception as hypothesis testing – action as experiments
But how do we think action will change our beliefs?
Searching, salience and saccades
( )s g
2 2
2 2
argmin ( ( ) ( )) ( )
argmin ( ( ) ( )) ( )
argmin ?
s
sa
s a g
a s a g
( )a t
Where do I expect to look?
( , ) ( | ) ( | )
[ ln ( ( ) | )] [ ( | ( ))]t t
H S H S m H S
E p s t m E H S s t
( ) [ ( | , )]H q S ( )s t S
saliencevisual inputstimulus sampling
Sampling the world to minimise uncertainty
Perception as hypothesis testing – saccades as experiments
( )t
Free energy principle minimise uncertainty
( ) argmin{ [ ( | , )]}t H q
( , ) ss a g ψ ω
Hidden states in the world Internal states of the agentSensations
argmin ( , )F s
argmin ( , )a F s μ a
( , ) xa ψ f ψ ω
ω
Action
External states
FluctuationsPosterior expectations
argmin [ ( | , )]H q
Prior expectations
,x p Frontal eye fields
ps
,v p
qs
,x pu
u
,x q
,x q
,v q
px
Pulvinar salience mapFusiform (what)
Superior colliculus
Visual cortex
oculomotor reflex arc
( )S
pxParietal (where)
a
200 400 600 800 1000 1200 1400-2
0
2Action (EOG)
time (ms)
200 400 600 800 1000 1200 1400
-5
0
5
Posterior belief
time (ms)
Saccadic fixation and salience maps
Visual samples
Conditional expectations about hidden (visual) states
And corresponding percept
Saccadic eye movements
Hidden (oculomotor) states
Beliefs about beliefs: beliefs about precision
If beliefs cause movement, how can I move when sensory evidence compels me to believe that I am not moving?
Sensory attenuation, illusions and agency
ss
ps
evix
14
8
8
( )
~ (0, )
~ (0, )
p is
s i e
i i x
s
x
ss
s
a
e I
e I
xω
x v
x x x ω
ω
ω
N
N
14
14
4
6
~ (0, )
~ (0, ) 8 ( )
~ (0, )
p is
s i e
i i ix
e e e
iv
e
s
x i i
v
s xs
s x x
x v xx
x v x
vv
v
e I
e I x v
e I
N
N
N
a
Generative process Generative model
Making your own sensations
x
ss
xv
v
ps
,v p
a
,v s
Motor reflex arc
thalamus
sensorimotor cortex
prefrontal cortex
ss
descending predictions
ascending prediction errors
descending modulation
High sensory attenuation
psss
ix
iv a
5 10 15 20 25 30
-0.5
0
0.5
1
1.5
2
prediction and error
Time (bins)5 10 15 20 25 30
-0.5
0
0.5
1
1.5
2
hidden states
Time (bins)
5 10 15 20 25 30
-0.5
0
0.5
1
hidden causes
Time (bins)5 10 15 20 25 30
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (bins)
perturbation and action
ex
ev
Low sensory attenuation
5 10 15 20 25 30
-0.5
0
0.5
1
1.5
2
prediction and error
time5 10 15 20 25 30
-0.5
0
0.5
1
1.5
2
hidden states
time
5 10 15 20 25 30
-0.5
0
0.5
1
hidden causes
time5 10 15 20 25 30
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time
perturbation and action
10 20 30 40 50 60-0.5
0
0.5
1
1.5
2prediction and error
Time (bins)10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2hidden states
Time (bins)
10 20 30 40 50 60-0.5
0
0.5
1
1.5
2hidden causes
Time (bins)10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2
Time (bins)
perturbation and action
10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2
hidden states
Force matching illusion
10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2
prediction and error
Time (bins) Time (bins)
Sensory attenuation
10 20 30 40 50 60
-0.5
0
0.5
1
1.5
hidden causes
Time (bins)10 20 30 40 50 60
-0.5
0
0.5
1
1.5
Time (bins)
perturbation and action
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
External (target) force
Self-
gene
rate
d(m
atch
ed) f
orce
External (target) force
Self-
gene
rate
d(m
atch
ed) f
orce
Simulated Empirical (Shergill et al)
Failures of sensory attenuation, with compensatory increases in non-sensory precision
A failure of sensory attenuation and delusions of control
10 20 30 40 50 60-0.5
0
0.5
1
1.5
2
2.5
3
3.5prediction and error
Time (bins)10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2
2.5
3
3.5hidden states
Time (bins)
10 20 30 40 50 60-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5hidden causes
Time (bins)10 20 30 40 50 60
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Time (bins)
perturbation and action
Thank you
And thanks to collaborators:
Rick AdamsAndre Bastos
Sven BestmannJean DaunizeauMark EdwardsHarriet BrownLee HarrisonStefan KiebelJames Kilner
Jérémie MattoutRosalyn Moran
Will PennyKlaas Stephan
And colleagues:
Andy ClarkPeter Dayan
Jörn DiedrichsenPaul FletcherPascal Fries
Geoffrey HintonJames HopkinsJakob Hohwy
Henry KennedyPaul Verschure
Florentin Wörgötter
And many others
( , ) ( | ) ( | )
[ ln ( ( ) | )] [ ( | ( ))]t t
H S H S m H S
E p s t m E H S s t
Searching to test hypotheses – life as an efficient experiment
Free energy principle minimise uncertainty
( ) argmin{ [ ( | , )]}t H q
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.