Transcript Input Layer of V1 for Macaque

Modeling Primary Visual Cortex
(of Macaque)
David W. McLaughlin
Courant Institute & Center for Neural Science
New York University
[email protected]
Santa Barbara Aug ‘01
Input Layer of V1 for Macaque
Modeled at :
Courant Institute of Math. Sciences
& Center for Neural Science, NYU
In collaboration with:
 Robert Shapley
Michael Shelley
Louis Tao
Jacob Wielaard
Visual Pathway: Retina --> LGN --> V1 --> Beyond
Why the Primary Visual Cortex?
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution --
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution -Detailed visual features of input signal;
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution -Detailed visual features of input signal;
Fine scale resolution available for possible representation;
Our Model
• A detailed, fine scale model of a layer of
Primary Visual Cortex;
• Realistically constrained by experimental data;
Our Model
• A detailed, fine scale model of a layer of
Primary Visual Cortex;
• Realistically constrained by experimental data;
• A “max-min’’ model -in that in its construction, we attempt to make
maximal use of experimental data, &
minimal use of posited architectural assumptions
which are not supported by direct experimental
evidence (such as Hebbian wiring schemes).
Overview: One Max-Min Model of V1
Overview: One Max-Min Model of V1
• A detailed fine scale model -- constrained in construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
Overview: One Max-Min Model of V1
• A detailed fine scale model -- constrained in construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
Overview: One Max-Min Model of V1
• A detailed fine scale model -- constrained in construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
• Complex Cells -- produced by weaker (and varied) LGN input,
together with stronger cortical excitation;
Overview: One Max-Min Model of V1
• A detailed fine scale model -- constrained in construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
• Complex Cells -- produced by weaker (and varied) LGN input,
together with stronger cortical excitation;
• Operates in a high conductance state -- which results from cortical
activity, is consistent with experiment, and makes integration
times shorter than synaptic times, an emergent separation of
temporal scales with functional implications;
Overview: One Max-Min Model of V1
• A detailed fine scale model -- constrained in construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
• Complex Cells -- produced by weaker (and varied) LGN input,
together with stronger cortical excitation;
• Operates in a high conductance state -- which results from cortical
activity, is consistent with experiment, and makes integration
times shorter than synaptic times, an emergent separation of
temporal scales with functional implications;
• Together with a coarse-grained asymptotic reduction -- which unveils
cortical mechanisms, and will be used to parameterize or ``scaleup’’ to larger more global cortical models.
Features of the Single Layer, Local Patch
Model
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic
• Excitation longer range than inhibition
Features of the Single Layer, Local Patch
Model
• Integrate & fire, point neuron model
• 16,000 neurons/sq mm
12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic
• Excitation longer range than inhibition
• Cortical inhibition dominant
Conductance Based Model
 = E,I
vj -- membrane potential
--  = Exc, Inhib
-- j = 2 dim label of location on
cortical layer
VE & VI -- Exc & Inh Reversal Potentials
Conductance Based Model
 = E,I
Schematic of Conductances
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
(cortico-cortical)
(LExc > LInh)
(Isotropic)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
Inhibitory Conductances:
gI(t) = gnoise(t) + gcortical(t)
(cortico-cortical)
(LExc > LInh)
(Isotropic)
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
•
Spatial phase  (relative to receptive field center)
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
•
•
Spatial phase  (relative to receptive field center)
Orientation  of edges.
Grating Stimuli
Standing & Drifting
Two Angles:
Angle of orientation -- 
Angle of spatial phase -- 
(relevant for standing gratings)
Orientation Tuning Curves
(Firing Rates Vs Angle of Orientation)
Spikes/sec 
Terminology:
• Orientation Preference
• Orientation Selectivity
Measured by “ Half-Widths” or “Peak-to-Trough”
Orientation Preference
Orientation Preference
• Model neurons receive their
orientation preference
from convergent LGN input;
Orientation Preference
• Model neurons receive their
orientation preference
from convergent LGN input;
• How does the orientation preference k of the kth
cortical neuron depend upon the neuron’s
location k = (k1, k2) in the cortical layer?
Cortical Map of
Orientation Preference
• Optical Imaging
Blasdel, 1992
----
• Outer layers (2/3) of V1
----

500 

• Color coded for angle of
orientation preference
 right
eye
 left
eye
Pinwheel
Centers
4 Pinwheel Centers
1 mm x 1 mm
Orientation Selectivity
While the model neurons receive their
orientation preference hardwired
from convergent LGN input;
they receive their orientation selectivity &
diversity from cortico-cortical activity;
Orientation Tuning Curves
__ __ __ Cortex off
Spikes/sec 
Ringach, Hawken & Shapley
McLaughlin,Shapley,Shelley & Wielaard
PNAS ‘00
Orientation Selectivity
(Measured by the “circular variance’’ of the tuning curves)
CV ~ 1, poorly tuned
~ 0, very selective
A measure of “height-to-trough”
Useful for population studies
Orientation Selectivity -- Population Behavior
(CV = Circular Variance of Tuning Curves)
CV ~ 1, poorly tuned
~ 0, very selective
Ringach, Hawken & Shapley
____ Excitatory
…… Inhibitory
McLaughlin,Shapley,Shelley & Wielaard
PNAS ‘00
Spatial Distributions of
Firing Rates and Orientation Selectivity
(Relative to Locations of Pinwheel Centers)
 Poorly tuned
Spikes/sec 
 Selective
Firing Rates
Circular Variance
(of Orientation Selectivity)
Experimental Evidence on
Spatial Distribution of
Orientation Selectivity
(relative to pinwheel centers)
• Maldonado, Gray, Goedecke
& Bonhoffer, Science ‘97
• In cat
• Data converted to CV’s
by M. Shelley
• Selectivity is diverse
• More selective (?) near pinwheels
Cortical Mechanism
For Spatial Distribution
Of Orientation Selectivity
• Discs of incoming
inhibition
• Radius set by axonal
arbors of inh. neurons
• While inhibition is
“local” in cortex,
• Near pinwheels, it is
“global” in orientation
Simple and Complex Cells
Simple cells respond linearly
to properties of the stimulus – a network property.
In a nonlinear network, “simple” is not so“simple”.
• Simple Cells :
Wielaard, Shelley, McLaughlin & Shapley,
to appear, J. Neural Science (2001)
• Simple & Complex Cells:
Tao, Shelley, McLaughlin & Shapley, in prep (2001)
Simple vs Complex Cells
• Simple cells respond ``linearly’’ to properties of
visual stimuli --
Simple vs Complex Cells
• Simple cells respond ``linearly’’ to properties of
visual stimuli -(i) Follow spatial phase of standing grating
Simple vs Complex Cells
• Simple cells respond ``linearly’’ to properties of
visual stimuli -(i) Follow spatial phase of standing grating
(ii) Respond temporally at the fundamental
(1st harmonic)
Simple vs Complex Cells
• Simple cells respond ``linearly’’ to properties of
visual stimuli -(i) Follow spatial phase of standing grating
(ii) Respond temporally at the fundamental
(1st harmonic)
• Complex cells -- phase insensitive &
large second harmonics
Experimental Measurements: Simple and Complex Cells
: Simple Cell

Phase
Time 
Model Results : Contrast Reversal
(For Optimal and Orthogonal Phase)
Cortex On
Membrane
Potential
Optimal
Phase
Firing
Rates
Orthogonal
Phase
Cortex Off
Mechanisms by which the Model Produces Simple Cells
Inputs to Cortical Cell:
• From LGN
(Frequency doubled at
orthogonal to optimal phase)
• From Other Cortical
Neurons
Mechanisms by which the Model Produces Simple Cells
Inputs to Cortical Cell:
• From LGN
(Frequency doubled at
orthogonal to optimal phase)
• From Other Cortical
Neurons (Also freq doubled,
because of averaging over
random phases -- whose
distribution is broad
(De Angelis, et al ‘99)
Mechanisms by which the Model Produces Simple Cells
Inputs to Cortical Cell:
• From LGN
(Frequency doubled at
orthogonal to optimal phase)
• From Other Cortical
Neurons (Also freq doubled,
because of averaging over
random phases -- whose
distribution is broad
(De Angelis, et al ‘99)
Mechanisms by which the Model Produces Simple Cells
Inputs to Cortical Cell:
• From LGN
(Frequency doubled at
orthogonal to optimal phase)
• From Other Cortical
Neurons (Also freq doubled,
because of averaging over
random phases -- whose
distribution is broad
(De Angelis, et al ‘99)
Cortical Overbalance for
Inhibition (Borg-Graham,
et al ‘98; Hirsch, et al ‘98;
Anderson, et al ‘00)
Cancellation
Simple Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
Simple Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
Simple Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
(iii) Balance produces linearity of simple cells
Simple Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
(iii) Balance produces linearity of simple cells
Indeed, this balance can be broken by pharmacologically
weakening inhibition -- converting simple cells to complex
Expt refs -- Sillito (‘74); Fregnac and Schulz (‘99);
Humphrey (‘99)
Simple vs Complex Cells
Continued
The model also contains complex cells (but, as yet,
not enough, and the complex cells are not selective
enough for orientation):
Simple vs Complex Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
Simple vs Complex Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
of) complex cells:
Simple vs Complex Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
of) complex cells:
(i) Weaker (and varied) LGN input;
Simple vs Complex Cells
• Recall mechanisms which produce (linear responses of)
simple cells:
(i) Averaging over spatial phases in
cortico-cortical terms;
(ii) Overbalance for inhibition in
cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
of) complex cells:
(i) Weaker (and varied) LGN input;
(ii) Stronger cortico-cortical excitation
(Abbott, et al, Nature Neural Science ‘98)
Simple vs Complex Cells
Continued
Drifting grating stimulation
Distributions of simple and complex cells
Expt -- Ringach, Shapley & Hawken
Model -- Tao, Shelley, McLaughlin & Shapley
Expts
Model
( Ringach, Shapley & Hawken)
(Tao, Shelley, McL & Shapley)
(Similar to earlier results
of De Valois, et al)
In V1, 40% Simple
(Preliminary)
In 4C, 55% Simple
1 mm x 1mm Local Patch of 4C
1 mm x 1mm
Active Model Cortex - High Conductances
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
====> gInh >> gExc
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
====> gInh >> gExc
• Consistent with experiment
Hirsch, et al,
J. Neural Sci ‘98;
Borg-Graham, et al, Nature ‘98;
Anderson, et al, J. Physiology ’00;
Lampl, et al, Neuron ‘99
Conductances Vs Time
• Drifting Gratings -- 8 Hz
• Turned on at t = 1.0 sec
• Cortico-cortical
excitation weak relative to LGN;
inhibition >> excitation
Distribution of Conductance
Within the Layer
Sec-1
<gT> = Time Average 
SD(gT) = Standard Deviation
Of Temporal Fluctuations 
Sec-1
Active Cortex - Consequences of High
Conductances
• Separation of time scales ;
Active Cortex - Consequences of High
Conductances
• Separation of time scales ;
• Activity induced g = gT-1 << syn (actually, 2 ms << 4 ms)
Active Cortex - Consequences of High
Conductances
• Separation of time scales ;
• Activity induced g = gT-1 << syn (actually, 2 ms << 4 ms)
• Membrane potential ``instantaneously’’ tracks
conductances on the synaptic time scale.
Definition of Effective Reversal Potential
V(t) ~ VEff(t) = [VE gEE(t) - | VI | gEI(t) ] [gT(t)]-1
Where gT(t) denotes the total conductance
Conductance Based Model
 = E,I
dv/dt = gT(t) [ v - VEff(t) ],
where gT(t) denotes the total conductance, and
VEff(t) = [VE gEE(t) - | VI | gEI(t) ] [gT(t)]-1
If [gT(t)] -1 << syn

v  VEff(t)
High Conductances in Active Cortex  Membrane Potential
Tracks Instantaneously “Effective Reversal Potential”
Active
Background
Effects of
Scale Separation
g = 2 syn
____(Red) = VEff(t)
____(Green) = V(t)
g = syn
g = ½ syn
Active Cortex - Consequences of High
Conductances
Thus, with this instantaneous tracking (on the
synaptic time scale),
cortical activity can convert neurons from
integrators to burst generators & coincidence
detectors.
Coarse-Grained Asymptotics
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
Cortical Map of
Orientation Preference
• Optical Imaging
Blasdel, 1992
----
• Outer layers (2/3) of V1
----

500 

• Color coded for angle of
orientation preference
 right
eye
 left
eye
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity,
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity,
• Together with an averaging over the irregular cortical
maps (such as spatial phase)
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity,
• Together with an averaging over the irregular cortical
maps (such as spatial phase)
• we derive a coarse-grained description in terms of the
average firing rates of neurons within each placquet

Uses of Coarse-Grained Eqs
Coarse-grained equations can be used to unveil the
model’s mechanism for
• Better selectivity near pinwheel centers
Spatial Distributions of
Firing Rates and Orientation Selectivity
(Relative to Locations of Pinwheel Centers)
 Poorly tuned
Spikes/sec 
 Selective
Firing Rates
Circular Variance
(of Orientation Selectivity)
m = {F + cEE KEE * m – cEI KEI * n }+
n = {F + cIE KIE * m – cII KII * n }+
---------------------------------------For ease, specialize :
cEE = cIE = cII = 0
m = {F – cEI KEI * n }+
n = {F }+ That is,
----------------------------------------------
m = {F – cEI KEI *  {F }+  }+
m() = {F () – cEI ’ KEI ( -’)  {F (’) }+  }+
----------------------------------------------m() = {F () – cEI  {F () }+  }+
FARR
m() = {F () – cEI  {’ F (’) }+  }+ NEAR
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
(ii) Balances for simple and complex cells
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
(ii) Balances for simple and complex cells
• Input-output relations at high conductance
One application of Coarse-Grained Equations
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
(ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
of distinct models of the cortex
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
(ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
of distinct models of the cortex
• Most importantly, much faster to integrate;
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better selectivity near pinwheel centers
(ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
of distinct models of the cortex
• Most importantly, much faster to integrate;
• Therefore, potential parameterizations for more
global descriptions of the cortex.
Conductance Based Model
 = E,I
-- 16,000 neurons per mm2
-- Locally, connections are isotropic
but
-- Long range coupling is
spatially heterogenous and orientation specific
Lateral Connections and Orientation -- Tree Shrew
Bosking, Zhang, Schofield & Fitzpatrick
J. Neuroscience, 1997
Scale-up & Dynamical Issues
for Cortical Modeling
• Temporal emergence of visual perception
• Role of temporal feedback -- within and between cortical
layers and regions
• Synchrony & asynchrony
• Presence (or absence) and role of oscillations
• Spike-timing vs firing rate codes
• Very noisy, fluctuation driven system
• Emergence of an activity dependent, separation of time
scales
• But often no (or little) temporal scale separation
Summary: One Max-Min Model of V1
• A detailed fine scale model -- constrained in its construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
• Complex Cells -- produced by weaker (and varied) LGN input,
together with stronger cortical excitation;
• Operates in a high conductance state -- which results from cortical
activity, is consistent with experiment, and makes integration
times shorter than synaptic times, a separation of temporal scales
with functional implications;
• Together with a coarse-grained asymptotic reduction -- which unveils
cortical mechanisms, and will be used to parameterize or ``scaleup’’ to larger more global cortical models.