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Gain Modulation
Huei-Ju Chen
Papers:
Chance, Abbott, and Reyes(2002)
E. Salinas & T. Sejnowski(2001)
E. Salinas & L.G. Abbott (1997, 1996)
Pouget & T. Sejnowski (2001)
Outline
• What is gain modulation?
• Gain modulation in the parietal cortex
(coordinate transformations)
• Gain modulation in Neglect
• Invariant visual responses from attentional
gain fields
• Gain modulation from background synaptic
Input
Introduction
• Gain modulation is a nonlinear way in
which neurons combine information from
two or more sources, which may be of
sensory, motor, or cognitive origin.
• One input affects the gain of the neuron to
the other input without modifying the
neuron’s receptive field properties.
– Salinas and Sejnowski, 2001
Gain Modulation In Neurons
Salinas & Sejnowski, 2001
Gain Fields: Gain Modulation
Without Changing RF
rx : retinotopic position
ex : eye position
Gain Fields
• Response of one neuron
r  f (t ) g (t ), f(t):weighted sum of input 1, g(t): input 2(modulator)
r  f ( xtarget  a ) g ( xgaze )
• The downstream response R
R  F (c1 xtarget  c2 xgaze )
– e.g. xtarget  xgaze
Gain Modulation in Cognition
• Coordinate transformations
– Modulatory quantity: gaze angle
• Translation-invariant object recognition and
size constancy
– Modulatory quantity: attention
• Motion processing
Gain Modulation
In Coordinate
Transformations:
Modulator: Gaze
Angle
Gain Modulation In Coordinate
Transformations
A Model of Multiplicative Neural
Responses in Parietal Cortex
Total external input to the neuron i:hi
hi  hiV ( x )  hiG ( y )
2
(
x

x
)
V
i
hiV ( x )  hmax
exp( 
)
2
2 V
hiG ( y )  mi yi  bi
• Synapse weights for recurrent connections
Wij  AE exp( 
( xi  x j )2
2
2
E
)  AI exp( 
( xi  x j ) 2
2
2
I
)
The firing rate of neuron i
ri  s[hi  Wij rj  hth ] ,s:slope of firing rate function
j
Salinas and Abbott, 1996
Simulations
One Model of Neglect (A
Coordinate Frame Syndrome)
• Neglect is a neurologic syndrome
characterized by a conspicuous inability to
react or respond to stimuli presented in the
hemispace contralateral to the lesion.
One Model of Neglect (A
Coordinate Frame Syndrome)
• Pouget & Sejnowski, 2001
a Ej 
1
,   8 or  8 (two maps)
1  exp( (e  e j ) /  )
aij  a
20
E
j

k 20
wik aiRk
==> product form
 ( ri  ri k ) 2 
wik  exp  

2
2



4
41 41
oi   wijkl n jkl a jkl
j 1 k 1 l 1
N ij  r ri  ee j  1
N ij  r ri  ee j   2
One Model of Neglect (A
Coordinate Frame Syndrome)
• The unilateral lesion is modeled by deleting
the two right maps.
si 
41

j 1,roij  ri
N ij aij
si is inversely proportional to RT.
Neglect (Contd.)
Neglect (Contd.)
Neglect (Contd.)
Invariant Visual Response From
Attentional Gain Field
V4: vi  Fi ( ai ; I )G ( y  bi ), G is a Gaussian function
IT: V  [ Wi vi   ] , Wi is established by Hebbian learning
i
Translation Invariance
Fi ( ai ; I )  [ Si ( ai ; I )]2  [Ci (ai ; I )]2
Scale Invariance
Fi S (ai ; I )  [ Si (ai ; I )] ; Fi C ( ai ; I )  [Ci ( ai ; I )]
Si ( ai ; I )   dxI ( x ) f i S ( x  ai ); Ci ( ai ; I )   dxI ( x ) f i C ( x  ai )
f i S ( x )  h cos( x1 /  )h cos( x2 /  )sin{ki [ x1 cos(i )  x2 cos(i )]}
f i C ( x )  h cos( x1 /  )h cos( x2 /  ) cos{ki [ x1 cos(i )  x2 cos(i )]}
Salinas and Abbott, 1997
Simulation
of Model
Network for
Images
Translated
Across
Visual Field
Simulation:
Images at
Different Scales
Salinas and Abbott, 1997
Gain Modulation From
Background Synaptic Input
• Chance, Abbott, and Reyes, 2002
• By introducing a barrage of excitatory and
inhibitory synaptic conductance that mimics
conditions encountered in vivo into
pyramidal cells in rat cortex, the gain of a
neuronal response to excitatory drive are
shown to be modulated by varying the level
of background synaptic input.
Chance, Abbott, and Reyes, 2002
Changing the
Level of
Background
Input
Modulates
Gain
Summary
• Gain modulation is a prominent feature of
neuronal activity recorded in behaving animals,
but the mechanism by which it occurs is still not
clear.
• Gain modulation is very close to multiplicative.
However, its essential feature is nonlinearity.
• Gain fields have been implicated in eye and
reaching movements, spatial perception, attention,
navigation, and object recognition.