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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 Fields
• Response of one neuron
• The downstream response R
– e.g.
target
( ) ( ), f(t):weighted sum of input 1, g(t): input 2(modulator)
( ) ( )gaze
r f t g t
r f x a g x
1 target 2 gaze( )R F c x c x
target gazex x
Gain Modulation in Cognition
• Coordinate transformations– Modulatory quantity: gaze angle
• Translation-invariant object recognition and size constancy– Modulatory quantity: attention
• Motion processing
Salinas and Abbott, 1996
A Model of Multiplicative Neural Responses in Parietal Cortex
• Synapse weights for recurrent connections
2
max 2
Total external input to the neuron i:
( ) ( )
( )( ) exp( )
2
( )
i
V Gi i i
V V ii
V
Gi i i i
h
h h x h y
x xh x h
h y m y b
2 2
2 2
( ) ( )exp( ) exp( )
2 2
The firing rate of neuron i
[ ] ,s:slope of firing rate function
i j i jij E I
E I
i i ij j thj
x x x xW A A
r s h W r h
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
20
20
2
2
4 41 41
1 1 1
1, 8 or 8 (two maps)
1 exp( ( ) / )
==> product form
( )exp
2
Ej
j
E Rij j ik i k
k
i i kik
i ijkl jkl jklj k l
ae e
a a w a
r rw
o w n a
One Model of Neglect (A Coordinate Frame Syndrome)
• The unilateral lesion is modeled by deleting the two right maps.
41
1,
is inversely proportional to RT.oij i
i ij ijj r r
i
s N a
s
Salinas and Abbott, 1997
Invariant Visual Response From Attentional Gain Field
2 2
V4: ( ; ) ( ), G is a Gaussian function
IT: [ ] , is established by Hebbian learning
Translation Invariance
( ; ) [ ( ; )] [ ( ; )]
Scale Invariance
( ; ) [ ( ; )] ;
i i i i
i i ii
i i i i i i
Si i i i i
v F a I G y b
V Wv W
F a I S a I C a I
F a I S a I F
1 2 1 2
1 2 1 2
( ; ) [ ( ; )]
( ; ) ( ) ( ); ( ; ) ( ) ( )
( ) cos( / ) cos( / )sin{ [ cos( ) cos( )]}
( ) cos( / ) cos( / )cos{ [ cos( ) cos( )]}
Ci i i
S Ci i i i i i i i
Si i i i
Ci i i i
a I C a I
S a I dxI x f x a C a I dxI x f x a
f x h x h x k x x
f x h x h x k x x
Chance, Abbott, and Reyes, 2002
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.
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.
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