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How Complex Cells Are Made in
a Simple Cell Network
Louis Tao
Courant Institute, New York University
Collaborators:
Michael Shelley (Courant, NYU)
Robert Shapley (CNS, NYU)
David McLaughlin (Courant, NYU)
Supported by grants from the Sloan Foundation, NSF DMS-9971813 & NIH EY 01472
Society for Neuroscience 2001
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
- selectivity for orientation, spatial frequency, spatial phase, …
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
- selectivity for orientation, spatial frequency, spatial phase, …
- dynamics of selectivity & diversity of selectivity
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
- selectivity for orientation, spatial frequency, spatial phase, …
- dynamics of selectivity & diversity of selectivity
• Large-scale computational model of Macaque V1
- Model of orientation selectivity & its dynamics
(McLaughlin et al., PNAS 2000)
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
- selectivity for orientation, spatial frequency, spatial phase, …
- dynamics of selectivity & diversity of selectivity
• Large-scale computational model of Macaque V1
- Model of orientation selectivity & its dynamics
(McLaughlin et al., PNAS 2000)
- Explanation of Simple Cells (Wielaard et al., JNS 2001 - WSMS)
Towards a Theory of the Visual Cortex
• Goal: Explain the response properties of cortical cells in the
V1 Network
- selectivity for orientation, spatial frequency, spatial phase, …
- dynamics of selectivity & diversity of selectivity
• Large-scale computational model of Macaque V1
- Model of orientation selectivity & its dynamics
(McLaughlin et al., PNAS 2000)
- Explanation of Simple Cells (Wielaard et al., JNS 2001 - WSMS)
- Now, Simple & Complex Cells in same basic circuit
Simple & Complex Classification
• Hubel & Wiesel (1962):
- Simple: approximately “linear”
- Complex: everything else
Simple & Complex Classification
• Hubel & Wiesel (1962):
- Simple: approximately “linear”
• Contrast Reversal: (1) sensitive dependence on spatial phase;
(2) temporal response at driving frequency
• V1: 40% Simple
• Likely necessary for visual perception
- Complex: everything else
• CR: (1) phase insensitive;
(2) frequency doubled
Orthogonal phase
Contrast Reversal at 8 Different Spatial Phases
DeValois et al. (Vis. Res. 1982)
Simple & Complex Classification
• Hubel & Wiesel (1962):
- Simple: approximately “linear”
• Contrast Reversal: (1) sensitive dependence on spatial phase;
(2) temporal response at driving frequency
• V1: 40% Simple
• Likely necessary for visual perception
- Complex: everything else
• CR: (1) phase insensitive;
(2) frequency doubled
• Simple-Complex Diversity
• Spectrum of Simple-Complex
Ringach et al. (IOVS 2001)
Drifting grating experiment
Simple & Complex Classification
• Surprisingly little work
– Chance, Nelson, and Abbott (Nat. NS 1999): Rate model,
assumed Simple cells to model Complex cells
– Wielaard, Shelley, McLaughlin, and Shapley (JNS 2001):
I & F network model, only Simple cells
Simple & Complex Classification
• Surprisingly little work
– Chance, Nelson, and Abbott (Nat. NS 1999): Rate model,
assumed Simple cells to model Complex cells
– Wielaard, Shelley, McLaughlin, and Shapley (JNS 2001):
I & F network model, only Simple cells
• Same Basic Circuit?
Features of Our Neuronal Network Model
• 16,000 Integrate & Fire, conductance-based, point neurons
1 square mm, local patch of Macaque 4Ca
Features of Our Neuronal Network Model
• 16,000 Integrate & Fire, conductance-based, point neurons
1 square mm, local patch of Macaque 4Ca
• Convergent LGN input confer orientation & spatial phase
preference (Reid & Alonso, 1995)
Regular Map of Orientation in Pinwheels
(Optical Imaging: Bonhoeffer & Grinvald,
1991; Blasdel, 1992; Maldonado et al., 1997
Random Map of Spatial Phase
(DeAngelis et al., 1999)
Features of Our Neuronal Network Model
• 16,000 Integrate & Fire, conductance-based, point neurons
1 square mm, local patch of Macaque 4Ca
• Convergent LGN input confer orientation & spatial phase
preference (Reid & Alonso, 1995)
• Local (< 500 mm) connections isotropic & nonspecific
(Fitzpatrick et al., 1985; Lund, 1987; Callaway &
Wiser, 1996)
Excitation longer range than inhibition
Features of Our Neuronal Network Model
• 16,000 Integrate & Fire, conductance-based, point neurons
1 square mm, local patch of Macaque 4Ca
• Convergent LGN input confer orientation & spatial phase
preference (Reid & Alonso, 1995)
• Local (< 500 mm) connections isotropic & nonspecific
(Fitzpatrick et al., 1985; Lund, 1987; Callaway &
Wiser, 1996)
Excitation longer range than inhibition
• Cortical inhibition dominant
(Borg-Graham et al., 1998; Hirsch et al., 1998;
Anderson et al., 2000)
Mechanisms Underlying Simple Cells
(WSMS 2001)
• Input: Rectification of convergent LGN input produces
frequency-doubled conductances at orthogonal phase
Where does this frequency-doubled input go?
Orthogonal Phase
Contrast Reversal: LGN Inputs
at 9 Different Spatial Phases
Wielaard et al. (2001)
Mechanisms Underlying Simple Cells
(WSMS 2001)
• Input: Rectification of convergent LGN input produces
frequency-doubled conductances at orthogonal phase
• Network: Isotropic coupling & sampling over many phases
produces frequency-doubled network conductances
Input Conductances
Mechanisms Underlying Simple Cells
(WSMS 2001)
• Input: Rectification of convergent LGN input produces
frequency-doubled conductances at orthogonal phase
• Network: Isotropic coupling & sampling over many phases
produces frequency-doubled network conductances
• Linearity: Large
intracortical
inhibition cancels
LGN input
Input Conductances
Mechanisms Underlying Complex Cells?
• Frequency-doubled firing rate:
reflection of frequency-doubled input
conductances?
Mechanisms Underlying Complex Cells?
• Frequency-doubled firing rate:
reflection of frequency-doubled input
conductances?
• Spatial phase insensitivity: Less LGN input?
Mechanisms Underlying Complex Cells?
• Frequency-doubled firing rate:
reflection of frequency-doubled input
conductances?
• Spatial phase insensitivity: Less LGN input?
• Different balance of excitation & inhibition?
Complex
I
I
E
E
V1
Inhibitory
Excitatory
LGN
Simple cells: Excitation mostly from LGN
Complex cells: Excitation mostly from network
Simple
Preferred phase
8 Different phases
Orthogonal phase
Model
(Tao, Shelley, McLaughlin &
Shapley)
In 4Ca, 50% Simple
Complex
Simple
Model
Experiment
(Tao, Shelley, McLaughlin &
Shapley)
( Ringach, Shapley & Hawken,
IOVS 2001)
(Similar to earlier results of De Valois, et al)
In V1, 40% Simple;
50% Simple in 4Ca
In 4Ca, 50% Simple
Complex
Simple
Spatial Distribution of Simple-Complex
Simple
1 mm
Orientation Selectivity Simple-Complex
• 16,000 neurons in 1 square mm
Complex
Orthogonal spatial phase
Preferred spatial phase
Input Conductances
Input Conductances
What have we achieved?
Network containing a diverse population of Simple and
Complex cells
What have we achieved?
Network containing a diverse population of Simple and
Complex cells
• Simple Cells arise from
• Isotropic coupling & sampling over many phases
• Strong network inhibition balances LGN excitation
What have we achieved?
Network containing a diverse population of Simple and
Complex cells
• Simple Cells arise from
• Isotropic coupling & sampling over many phases
• Strong network inhibition balances LGN excitation
• Complex Cells arise from
• Weaker LGN input
• Stronger cortical excitation
A Neuronal Network Model of V1 (4Ca)
• Simple & Complex
• Orientation Selectivity
• Dynamics of Orientation
Tuning
Thanks to Michael Shelley, Robert Shapley
& David McLaughlin
Input Conductances
Total
Inhibitory
Excitatory
LGN
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)
Lateral Connections and Orientation -- Tree Shrew
Bosking, Zhang, Schofield & Fitzpatrick
J. Neuroscience, 1997
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
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 Map of
Orientation Preference
• Optical Imaging
Blasdel, 1992
----
• Outer layers (2/3) of V1
----

500 m

• Color coded for angle of
orientation preference
 right
eye
 left
eye