Precision in Cortical Message Passing
Rosalyn J. Moran
Wellcome Trust Centre for Neuroimaging
1st Workshop on the Free Energy Principle, ION, UCL, July 5th 2012.
Outline
Predicting & Estimating Precision under the Free Energy Principle
- Laplace and Mean Field Assumptions
Hypothesised Neuronal Implementation & the role of Neuromodulators
- Gain effects on primary neurotransmission
Cholinergic Neuromodulation & Certainty Effects on Auditory mismatch negativity
- Theoretical simulation of perception
Testing Cholinergic Neuromodulation
- DCM characterization of Event Related Responses
Outline
Predicting & Estimating Precision under the Free Energy Principle
- Laplace and Mean Field Assumptions
Hypothesised Neuronal Implementation & the role of Neuromodulators
- Gain effects on primary neurotransmission
Cholinergic Neuromodulation & Certainty Effects on Auditory mismatch negativity
- Theoretical simulation of perception
Testing Cholinergic Neuromodulation
- DCM characterization of Event Related Responses
Predicting & Estimating Precision under the Free
Energy Principle
Hierarchical, Dynamic & Uncertain causes in the environment generate sensory signals
Different Levels of the hierarchy and/or different sensory signals
may confer more precise Information
The Environment
Hierarchical, Dynamic
v (2) = h
v (1) = g(x (1), v (2), q )
x (1) = f (x (1), v (2), q )
y = g(x (1), v (1), q )
x (1) = f (x1, v (1), q )
The Environment
Hierarchical, Dynamic & Uncertain causes generate sensory signals
v (2) = h + w v(3)
v (1) = g(x (2), v (2), q ) + w v(2)
x (2) = f (x (2), v (2), q ) + w x(2)
y = g(x (1), v (1), q ) + w v(1)
x (1) = f (x1, v (1), q ) + w x(1)
y
y
The Inversion
Estimate: Hierarchical, Dynamic & Uncertainty of sensory signals to minimise the surprise
of the sensory signals
v (2) = h + w v(3)
v (1) = g(x (2), v (2), q ) + w v(2)
Minimise Free Energyx (2) = f (x (2), v (2), q ) + w x(2)
H ( y | m)    p( y | m) ln p( y | m)dy
(1)
(1)
(1)
H ( y | m)    py( =
y (tg(x
) | m)dt, v , q ) + w v
F (t )   p ( y (t ) x| m) = f (x , v , q ) + w x
(1)
1
(1)
Minimise Surprise
Time averaged Surprise(Ergodicity)
(1)
F (t )   p ( y (t ) | m)  KL(q ( ) || p( | y, m))
Minimise F at every point in time
States, parameters & noise
The Brain’s Response to y
… A Tractable Problem
y
y
Outline
Predicting & Estimating Precision under the Free Energy Principle
- Laplace and Mean Field Assumptions
Hypothesised Neuronal Implementation & the role of Neuromodulators
- Gain effects on primary neurotransmission
Cholinergic Neuromodulation & Certainty Effects on Auditory mismatch negativity
- Theoretical simulation of perception
Testing Cholinergic Neuromodulation
- DCM characterization of Event Related Responses
y
Minimising Free Energy
F (t )   p( y (t ) | m)  KL(q( ) || p( | y, m))
The Laplace Assumption: The brain assumes gaussian random fluctuations
v (m) = h + w v(m+1)
...
v (i-1) = g(x (i), v (i), q ) + w v(i)
0 1 5 10 15 20 25
x (i) = f (x (i), v (i), q ) + w x(i)
...
y = g(x (1), v (1), q ) + w v(1)
0 1 5 10 15 20 25
x (1) = f (x1, v (1), q ) + w x(1)
Smooth noise correlations within levels
1 5 10 15 2025
Markov properties between levels
w ~ N(0, S(x, v, g ))
p(y, x, v) = p(y | x, v)p(x, v)
S=V Ä S
p(x, v) = p(v )Õ p(x (i) | v (i) )p(v (i) | x (i+1), v (i+1) )
S-1 = P
m-1
m
i=1
Gradients a function of error terms weighted by the precisions at each level:
How might precisions be encoded?
Gradients of Free Energy
Precision Dependent
x (1,v)
y
Superficial pyramidal cells
x (1,x)
x (2,v)
Backward predictions
Forward prediction error
y(t)
Deep pyramidal cells
m
(1,x)
m (1,v)
x (i,v) = P(i,v) (m (i-1,v) - f (i,v) )
x (i,x) = P(i,x) (Dm (i,x) - f (i,x) )
Perceiving multiple hierarchical levels together:
errors can have a greater or lesser effect
A multiplicative term that stays within levels:
Candidate mechanisms: local lateral inhibition & neuromodulators
Gain control at superficial pyramidal cells y
Neuromodulators: Anatomically deployed
to provide input in multiple regions
Eg Sarter et al. 2009
Local Glutamate & GABA
Long Range Glutamate
Diffuse projections
Neuromodulators
Acetylcholine
Dopamine
Gain control at superficial pyramidal cells y
Neuromodulators: Physiologically equipped to provide gain control
Cholinergic
Projections
from Basal
Forebrain
Activity at muscarinic receptors
enhances EPSPs through K-current modulation
Dopaminergic
Projections
from VTA/SNc
Activity at D1 receptors
stimulates adenylyl cyclase
modulating postsynaptic currents
Gain control at superficial pyramidal cells y
Neuromodulators: Physiologically equipped to provide gain control
Dopaminergic
Projections
from VTA/SNc
Cholinergic
Projections
from Basal
Forebrain
Dendritic spine
Presynaptic
terminals
m (i-1,v)
x
f (i,v )
error
P
(i,v )
Excitatory (AMPA) receptors
Modulatory receptor
Inhibitory (GABAA) receptors
(i,v )
precision
Precision-weighted error
Outline
Predicting & Estimating Precision under the Free Energy Principle
- Laplace and Mean Field Assumptions
Hypothesised Neuronal Implementation & the role of Neuromodulators
- Gain effects on primary neurotransmission
Cholinergic Neuromodulation & Certainty Effects on Auditory mismatch negativity
- Theoretical simulation of perception
Testing Cholinergic Neuromodulation
- DCM characterization of Event Related Responses
Testing error precision modulation by Acetylcholine:
The Framework
Recognition Dynamics
m = Dm - e T x
u
7 Auditory Stimuli:
Pure tones presented in mini-blocks
Simulate Experiment
Under Placebo
& Cholinergic Enhancement
Freq
time
Mismatch Negativity
~150 ms
Testing error precision modulation by Acetylcholine:
The Sensory Data
Recognition Dynamics
m = Dm - e T x
u
There was a particular
sound
The sound has dynamics
determined by properties,
Frequency and Amplitude
~y
Sensations
Testing error precision modulation by Acetylcholine:
The Sensory Data
C =4
A two level hierarchy
Freq
time
v (1) = h (t) + w v(2)
é (1)
x = q f x +ê v
êë 0
(1)
(1)
ù
ú + w x(1)
úû
y(t) = q g x (1) + w v(1)
~y
Sensations
é -1/ 16 4 / 16 ù
é 0 1 ù
qg = ê
ú qf =ê
ú
ë C 0 û
ë -2 / 16 -1/ 16 û
Testing error precision modulation by Acetylcholine:
The Sensory Data
A two level hierarchy
C=2
Freq
time
v (1) = h (t) + w v(2)
é (1)
x = q f x +ê v
êë 0
(1)
(1)
ù
ú + w x(1)
úû
y(t) = q g x (1) + w v(1)
~y
Sensations
é -1/ 16 4 / 16 ù
é 0 1 ù
qg = ê
ú qf =ê
ú
ë C 0 û
ë -2 / 16 -1/ 16 û
Testing error precision modulation by Acetylcholine:
The Inversion: assume different precision estimates
Freq
~y
time
Sensations
w v(1) = N (0,g -1 )
v (1) = h (t) + w v(2)
é (1)
x = q f x +ê v
êë 0
(1)
(1)
y(t) = q g x (1) + w v(1)
ù
ú + w x(1)
úû
p(g ) = N (mg ,exp(-4))
p(g ) = N (mg + 2,exp(-(4 + 2)))
Placebo
ACh
Testing error precision modulation by Acetylcholine:
The Recognition Dynamics under different precision estimates
w v(1) = N (0,g -1 )
~y
Freq
time
p(g ) = N (mg ,exp(-4))
Sensations
p(g ) = N (mg + 2,exp(-(4 + 2))) ACh
Simulated ERP ACh
Simulated ERP Placebo
Precision weighted PE
80
80
d1
d2
d10
60
40
60
40
20
20
0
0
-20
-20
-40
-40
-60
-60
-80
Placebo
0
50
100
150
200
Time (msec)
250
300
-80
0
50
100
150
Time (msec)
200
250
300
Testing error precision modulation by Acetylcholine:
The MMN itself under different precision estimates
Simulated ERP ACh
Simulated ERP Placebo
80
d1
d2
d10
60
40
60
40
20
20
0
0
-20
-20
-40
-40
-60
-60
-80
0
50
100
150
200
Time (msec)
Simulated MMN Placebo
Precision weighted PE
Precision weighted PE
80
25
20
15
10
5
0
-5
Certain
Environment
Until oddball
250
300
-80
0
50
100
150
Time (msec)
200
250
Simulated MMN ACh (more Precision)
More
Certain
Environment
Until oddball
300
Outline
Predicting & Estimating Precision under the Free Energy Principle
- Laplace and Mean Field Assumptions
Hypothesised Neuronal Implementation & the role of Neuromodulators
- Gain effects on primary neurotransmission
Cholinergic Neuromodulation & Certainty Effects on Auditory mismatch negativity
- Theoretical simulation of perception
Testing Cholinergic Neuromodulation
- DCM characterization of Event Related Responses
Testing error precision modulation by Acetylcholine:
7 Auditory Stimuli:
Pure tones presented in mini-blocks
Real Experiment
Under Placebo
& Cholinergic Enhancement
Freq
time
Mismatch Negativity
~150 ms
Scalp Effects: MMN
Simulated MMN Galantamine (more Precision)
Simulated MMN Placebo
Precision weighted PE
More Certain
Environment
Until oddball
25
20
15
Certain
Environment
Until oddball
10
5
0
-5
Recorded MMN Placebo
2.5
channel C21
2
1.5
1
0.5
0
-0.5
-1
-1.5
*
*
Recorded MMN Galantamine
Physiological & Hierarchical Predictions
Recall:
x (1,v)
Superficial pyramidal cells
x (1,x)
x (2,v)
Backward predictions
Forward prediction error
y(t)
Deep pyramidal cells
m
(1,x)
A multiplicative term that stays within levels:
Candidate mechanisms: neuromodulators
m (1,v)
x (i,v) = P(i,v) (m (i-1,v) - f (i,v) )
x (i,x) = P(i,x) (Dm (i,x) - f (i,x) )
Acetylcholine: Where does it affect network processing?
What region?
What layer?
Gain Modulation at
Supragranular
Pyramidal Cells
IFG
IFG
Inhibitory
interneuron
 ( x)
 (v)
Superficial pyramidal
MTG
A1
A1
MTG
 (v)
Spiny stellate
Deep
pyramidal
 ( x)
Backward connections
Forward connections
Gain Modulation
at Deep Pyramidal Cells
Forward (Bottom-up) Connection
Backward (Top-Down) Connection
Acetylcholine: Where does it affect network processing?
What region?
What layer?
IFG
MTG A1
MTG
A1
IFG
MTG
A1
A1 MTG
Forward (Bottom-up) Connection
Backward (Top-Down) Connection
DCM
Electromagnetic
forward model:
neural activity EEG
MEG
LFP
Hemodynamic
forward model:
neural activity BOLD
Time Domain Data
dx
 F ( x , u,  )
dt
Time Domain ERP Data
…
Neural state equation:
fMRI
simple neuronal model
Slow time scale
Neural Mass Model
EEG/MEG
complicated neuronal model
Fast time scale
Acetylcholine: Where does it affect network processing?
What region?
What layer?
IFG
MTG A1
MTG
A1
IFG
MTG
A1
A1 MTG
Forward (Bottom-up) Connection
Backward (Top-Down) Connection
DCM for ERPs : Canonical Microcircuit
Inhibitory interneuron

Superficial pyramidal
( x)

(v)
 (v)
Spiny stellate
Deep pyramidal
 ( x)
Backward connections
Forward connections
Acetylcholine: Bayesian Model Selection
Intrinsic Modulation (models 1-6); Extrinsic Modulation (models 7-10)
IFG
A1
A1
MTG
A1
MTG
IFG
IFG
MTG
A1
A1
Relative Log Model Evidence
IFG
MTG
IFG
A1
A1
MTG
IFG
MTG
IFG
MTG
MTG
A1
MTG
A1
MTG
IFG
A1
MTG
IFG
IFG
A1
A1
∆F = 153
800
600
400
200
0
Forward Connection
Backward Connection
IFG
IFG
A1
Model 10
A1
A1
A1
MTG
MTG
MTG
MTG
Model 8
IFG
IFG
MTG
A1
A1
MTG MTG
Model 9
IFG
IFG
A1
A1
Model 7
1000
IFG
MTG MTG
MTG
MTG
1A
Model 6
Model 4
Model 3
IFG
IFG
MTG
A1
Model 5
MTG
Model 3
Model 2
IFG
IFG
Model 1
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10
Acetylcholine: Direction of Gain Modulation
In A1
Inhibitory
interneuron
 ( x)
 (v)
Superficial pyramidal
 (v)
Spiny stellate
Deep
pyramidal
 ( x)
Backward connections
Forward connections
w v(1) = N (0,g -1 )
p(g ) = N (mg ,exp(-4))
Superficial Pyramidal Cell Gain
Modulatory Effect of Galantamine
Gain Modulation at
Supragranular
Pyramidal Cells
0.06
*
0.05
0.04
0.03
0.02
0.01
Placebo
Baseline
Placebo
p(g ) = N (mg + 2,exp(-(4 + 2))) ACh
Galantamine
Summary
Precision estimates enable Bayes optimal perception
- Hierarchical inference enables different precision effects at different
levels
- Precision estimates control the impact of errors in Free Energy
minimisation under the Laplace Assumption
Neuromodulators are anatomically & physiologically equipped to signal
precision in this scheme
Neuromodulatory systems could control precision at different hierarchical
levels
Cholinergic Neuromodulation controls gain in superficial pyramidal cells in
early sensory regions; conforming to Free Energy Predictions of enhanced
precision on sensory prediction errors
Thank You
Acknowledgments
Karl Friston
Ray Dolan
Klaas Enno Stephan
Mkael Symmonds
Nicholas Wright
Pablo Campo
Methods Group
Emotion Group