A proposal for the function of
canonical microcircuits
André Bastos
July 5th, 2012
Free Energy Workshop
Outline
• Review of canonical (cortical) microcircuitry
(CMC)
• Role of feedback connections
– Driving or modulatory?
– Excitatory or inhibitory?
• Recapitulation of free energy principle
– Derive the predictive coding CMC
• Empirical vs. predictive coding CMC
• Frequency dissociations in the CMC
What does a CMC need to do, in principle?
• Amplify weak inputs from thalamus or other
cortical areas
– LGN provides only 4% of all synapses in V1 granular
layer
• Maintain a balance of excitation and inhibition
• Select meaningful signals from a huge number of
inputs (on average 10,000 synapses onto a single
PY cell)
• Segregate outputs from and inputs to a cortical
column
A first proposal on the CMC
• Amplify thalamic inputs through
recurrent connections
• Maintain a balance of exc./inh.
• Segregate super/deep
Douglas and Martin, 1991
Quantitative study of C2 barrel cortex
Lefort et al., 2009
Information flow summarized
Lefort et al., 2009
Spread of feedforward activity through the CMC
L1
Extrastriate (V2)
L2/3
4A/B
4Ca/B
L5
L6
LGN
Pulvinar
LGN
www.brainmaps.org
Drivers vs. modulators
The corticogeniculate feedback
connection displays modulatory
synaptic characteristics.
This suggested that corticocortical feedback is also
modulatory…
Sherman and Guillery, 1998, 2011
The “straw man”
• Feedforward connections are driving
– V1 projects monosynaptically to V2, V3, V3a, V4, and MT
– In all cases, when V1 is reversibly inactivated, neural
activity in the recipient areas is strongly reduced or
silenced (Girard and Bullier, 1989; Girard et al., 1991a,
1991b, 1992, Schmid et al., 2009)
• Feedback connections are modulatory
– Synaptic characterization of Layer 6 -> LGN feedback
• Longstanding proposal: corticocortical feedback
connections are also modulatory (not an unreasonable
assumption)
At least some feedback connections
are not just modulatory…
Feedforward connections A1->A2
Feedback connections A2->A1
De Pasquale and Sherman, 2011, Covic and Sherman, 2011
Feedback: inhibitory or excitatory?
• On theoretical grounds, we would predict
inhibitory
– Higher-order areas predict activity of lower areas.
When activity is predictable it evokes a weaker
response due to inhibition induced by higher areas
• Neuroimaging studies (repetition suppression,
fMRI, MMN) suggests inhibitory role for feedback
• Electrophysiology with cooling studies are mixed
Inhibitory corticogeniculate and intrinsic feedback
Silence V1
Stimulate V1
dLGN
Olsen et al., 2012
Corticocortical feedback targets L1
Shipp, 2007
Inhibitory “hot spot” in L1
Meyer et al., 2011
L1 cells are functionally active and
inhibit PY cells in L2/3 and L5/6
Shlosberg et al., 2006
Spread of feedback activity through the CMC
L1
L2/3
Higher-order cortex
4A/B
4Ca/B
L5
L6
LGN
www.brainmaps.org
Anatomical and functional constraints
??? canonical microcircuit for predictive coding ???
Predictive coding constraints
The Free Energy Principle, summarized
• Biological systems are homoeostatic
– They minimise the entropy of their states
• Entropy is the average of surprise over time
– Biological systems must minimise the surprise associated
with their sensory states at each point in time
• In statistics, surprise is the negative logarithm of
Bayesian model evidence
– The brain must continually maximise the Bayesian
evidence for its generative model of sensory inputs
• Maximising Bayesian model evidence corresponds to
Bayesian filtering of sensory inputs
– This is also known as predictive coding
What generative model does the brain use???
Hierarchical Dynamical Causal Models
Advantage: Extremely general models that grandfather most parametric models
in statistics and machine learning (e.g., PCA/ICA/State-space models)
Output
𝑦 = 𝑔 𝑥, 𝑣 + 𝑧
Observation noise
Hidden states
𝑥 = 𝑓 𝑥, 𝑣 + 𝑤
State noise
Inputs
Friston, 2008
Sensations are caused by a complex world with
deep hierarchical structure
input
v2
Level 0
Level 1
x2
v1
𝑣1 = 𝑔 𝑥 2, 𝑣 2 + 𝑧 2
(cause)
(state)
(cause)
Level 0
x1
𝑥1 = 𝑓 𝑥1, 𝑣1 + 𝑤 2
(state)
s
𝑠= …
(sensation)
A simple example: visual occlusion
A simple example: visual occlusion
Hierarchical causes on sensory data
input
v2
x2
v1
x1
s
𝑥 2 = 𝑓 𝑥 2, 𝑣 2 + 𝑤 2 𝑣1 = 𝑔 𝑥 2, 𝑣 2 + 𝑧 2
(cause)
(state)
(cause)
(state)
(sensation)
Perception entails model inversion
Hierarchical generative model
v(3)
v (2)
x(2)
x (2)
v(2)
v (1)
 x(1)
x (1)
 v(1)
Recognition Dynamics
Expectations:
 x( i )  D  x( i )   x ( i )   ( i )
(1)
vx(0)
Prediction errors:
Hierarchical generation
v( i )  D v( i )   v ( i )   ( i )   v( i 1)
 v( i )   (vi ) ( v( i 1)  g ( i ) (  x( i ) , v( i ) ))
 x( i )   (xi ) (D  x( i )  f ( i ) (  x( i ) , v( i ) ))
Mind meets matter…
Hierarchical generative model
Hierarchical predictive coding
Bottom-up
prediction errors
v(3)
x(2)
v(2)
 x(1)
 v(1)
 v(1)
 x(1)
 v(2)
 x(2)
 v(3)
v (2)
x (2)
v (1)
x (1)
(1)
vx(0)
 v(0)
 x(1)
 v(1)
 x(2)
 v(2)
Hierarchical generation
Top-down predictions
𝑠 =𝑣
(0)
(0)
= 𝜇𝑣
Recognition Dynamics
Canonical microcircuit for predictive coding
Forward prediction error
 (vi 1)

Expectations:
Prediction errors:
v( i )  D v( i )   v ( i )   ( i )   v( i 1)
 x( i )  D  x( i )   x ( i )   ( i )
 v( i )   (vi ) ( v( i 1)  g ( i ) (  x( i ) , v( i ) ))
( i 1)
v
g (i 1)
 v( i )
 x( i )
 v( i )
 x( i )
Forward
prediction
error
 ( v ,i )
 x( i )   (xi ) (D  x( i )  f ( i ) (  x( i ) , v( i ) ))
 v( i )
f (i )
 x( i )
g (i ) Backward predictions
Backward
predictions
Canonical microcircuit from
anatomy
Canonical microcircuit from
predictive coding
Forward
prediction error
 (vi 1)
v(i 1)
Forward
prediction error
 ( v ,i )
g (i 1)
 v( i )
 x( i )
 v( i )
 x( i )
 v( i )
f (i )
 x( i )
g (i )
Haeusler and Maass (2006)
Backward predictions
Bastos et al., (in review)
Backward predictions
Spectral asymmetries between superficial and deep cells
Rate of change
of units encoding
expectation (send
feedback)
Prediction error
units (send feedforward messages)
0.3
1
2
0.25
0.2
v(i 1) ( )
2
superficial
v(i 1)
0.15
0.1
 v( i )
 x( i )
0.05
0
0
x 10
20
40
60
80
frequency (Hz)
100
120
-4
 x( i )
 v( i )
2
Fourier transform
v(i ) ( ) 
2
2
1 (i 1)

(

)
v
2
 v( i )

1
0
0
20
40
60
80
frequency (Hz)


deep
(i )
x
100
120
Different oscillatory modes for
different layers
V1
V2
V4
Buffalo, Fries, et al., (2011)
Unpublished data
We apologize, but cannot share this
slide at this point
Unpublished data
We apologize, but cannot share this
slide at this point
Unpublished data
We apologize, but cannot share this
slide at this point
Unpublished data
We apologize, but cannot share this
slide at this point
Integration of top-down and bottom-up through
oscillatory modes?
alpha/beta
gamma
???
???
(𝑖+1)
𝜉𝑣
=
prediction error
Π𝑣
(𝑖+1)
precision
(𝝁𝒗
state
𝒊
−𝒈
𝒊+𝟏
)
higher-level prediction
Integration of top-down and bottom-up streams
Forward
prediction error
 (vi 1)

Forward
prediction error
 ( v ,i )
( i 1)
v
g (i 1)
Backward predictions
 v( i )
 x( i )
 v( i )
 x( i )
 v( i )
f (i )
 x( i )
g (i )
(𝑖+1)
𝜉𝑣
=
prediction error
Π𝑣
(𝑖+1)
precision
Backward predictions
(𝜇𝑣
𝑖
state
−𝑔
𝑖+1
)
higher-level prediction
Canonical microcircuits and DCM
V1 (primary visual cortex)
 (s)
 (v )
V4 (extrastriate visual area)
Feedback connections
Feedforward connections
Intrinsic connections
 ( x)
 (v)
 (v)
 ( x)
 (v )
 ( x)
local fluctuations
local fluctuations
Unpublished data
We apologize, but cannot share this
slide at this point
Unpublished data
We apologize, but cannot share this
slide at this point
Conclusions
• Repeating aspects of cortical circuitry suggest a “canonical
microcircuit” exists to perform generic tasks that are
invariant across cortex
• Traditional roles for feedback pathways are being
challenged by newer data
• Predictive coding offers a clear hypothesis for the role of
feedback and feedforward pathways
• Predicts spectral asymmetries which may be important for
how areas communicate
• In short: the function of CMCs may be to implement
predictive coding in the brain
• These predictions might soon be testable with more
biologically informed (CMC) DCMs
Acknowledgements
• Julien Vezoli
• Conrado Bosman, Jan-Mathijs Schoffelen,
Robert Oostenveld
• Martin Usrey, Ron Mangun
• Pascal Fries
• Rosalyn Moran, Vladimir Litvak
• Karl Friston
Behaviors of a realistic model for oscillations
• Laminar segregation and independence of
gamma and beta rhythms
Roopun 2008
Where do HDMs come from?
Friston 2008