v1 computational theory - center for neural sciencev1 computational theory lateral view...
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V1 Computational Theory
Lateral view
Retinogeniculate visual pathway
Ventral view
optic nerve
optic chiasm
optic tract
LGN
optic radiation
primary visual cortex
Retinogeniculate visual pathway
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Stimulus drive & response selectivity
V1 orientation tuning
Neu
ral r
espo
nse
(spi
kes/
sec)
Stimulus orientation (deg)
Simple cell
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Complex cell
Hubel & Wiesel movie
V1 physiology
Simple cells:• orientation selective• some are direction selective• some are disparity selective• monocular or binocular• separate ON and OFF subregions• length summation(best response to long bar)
Complex cells:• orientation selective• some are direction selective• some are disparity selective• nearly all are binocular• no separate ON and OFF subregions• length summation
Hypercomplex cells:end-stopping (best response to short bar)
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No stimulus in receptive field: no response
Non-preferred stimulus: no response
Preferred stimulus: large response
Orientation selectivity model
Stimulus: vertical bar
Responses of each of severalorientation tuned neurons.
Peak (distribution mean) codesfor stimulus orientation.
Distributed representation of orientation
Broad tuning can code for small changes
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Neural code depends on multiple factors
linearweighting function
rectification
firing ratestimulus
Complementaryreceptive fields
Rectification and squaring
Rectification and squaring
Rectification approximates relationship between membrane potential and spiking
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Greg DeAngelis
Complex cells: theory
Complex cells & position invarianceOriented stimulus as seen by both subunits at two different locations:
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Theory of spatial pattern analysis by the visual system
Input image(cornea)
“Neural image”(retinal ganglion cells)
Neural image: retinal ganglion cell responses
Array of center-surround receptive fields
Neural image: simple cell responses
Input image(cornea)
“Neural image”(V1 simple cells)
Array of orientation-selective receptive fields
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Lots of neural images: V1 simple cells
A
B
C
Lots of neural images
V1 simple cells
V1 complex cells
Psychophysical/perceptual evidence for spatial-frequency and orientation selective channels
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++
Orientation selective adaptation
Orientation selective adaptation
+
+
Orientation selective adaptation
+
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Normalization in monkey V1
Response saturation and phase advance
25%
50%
0 1540
Time (ms)
Res
pons
e (s
p/s)
100%
12.5%
2
5
10
20
50
100
Ampl
itude
(sp/
s)
5 10 20 50 100-90
-45
0
Contrast (%)
Rel
ativ
e ph
ase
(deg
)
Time (ms)
Resp
onse
(sp/
s)
Contrast (%)
Rela
tive
pha
se (d
eg)
Am
plit
ude
(sp/
s)
Can no longer discriminate orientations near vertical
Failure of invariance with saturation?
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10 20 50 100
0.5
1
2
5
10
20
50
Contrast of grating 1 (%)
Res
pons
e A
mpl
itude
(sp
/s)
10 20 50 100
Contrast of grating 2 (%)
6.25%
25%
50%
6.25% 25%
0%
50%
6130
76
Time (ms)
Res
pons
e (s
p/s)
0%
0
Masking
Normalization model
Σ( )normalizedresponse
(unnormalized response)2
unnormalized 2responses + σ
2
=
Response saturation and cross-orientation suppression
25%
50%
0 1540
Time (ms)
Res
pons
e (s
p/s)
100%
12.5%
2
5
10
20
50
100
Ampl
itude
(sp/
s)
5 10 20 50 100-90
-45
0
Contrast (%)
Rel
ativ
e ph
ase
(deg
) Contrast (%)
Am
plit
ude
(sp/
s)
r = α c2
c2 +σ 2
10 20 50 100
0.5
1
2
5
10
20
50
Contrast of grating 1 (%)
Res
pons
e A
mpl
itude
(sp
/s)
10 20 50 100
Contrast of grating 2 (%)
6.25%
25%
50%
6.25% 25%
0%
50%
6130
76
Time (ms)
Res
pons
e (s
p/s)
0%
0
r = α ct2
ct2 + cm
2 +σ 2
Resp
onse
am
plit
ude
(sp/
s)
Contrast of grating 1 (%)
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Ratio of responses to pref and non-pref directions constant overfull range of contrasts.
Contrast invariance
Contrast
Resp
onse
(spi
kes/
sec)
Tolhurst & Dean (1980) Model
Surround suppression
CRF
SurroundSurround ck
sk
CRF
Surround
0 < β < 1 surround suppression
80
60
40
20
0
0 1 2 3 4 5 6452l021.p05
Grating patch diameter (deg)
Res
pons
e (im
p/se
c)
Suppression
Surrounddiameter
Optimaldiameter
Surround suppression
CRF
SurroundSurround ck
sk
CRF
Surround
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Psychophysical/perceptual evidence for normalization
Masking
Target Surround masking
Overlay masking
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Canonical computation hypothesis: normalization in other brain areas
Light adaptation in the retina (revisited)
R =α ItIt + Ib +σ
1 10 1000
50
100
150
200
1 10 100ORN response (spikes/sec)
PN r
espo
nse
(spi
kes/
sec)
Normalization in fruit fly olfaction
R = α Itn
Itn + Im
n +σ n
Mask odor Test odorORN: olfactory receptor neuronPN: projection neuron
Test only Mask + Test
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Also...
•Visual cortical areas V4 (pattern), MT (motion perception), and IT (object recognition).
•Other sensory modalities: auditory cortex; multisensory integration (visual motion and vesibular system) in MST.
•Encoding of value in posterior parietal cortex.•Superior colliculus: saccade averaging.•Attention: modulation of activity in visual cortex.
Why normalize?
• Limited dynamic range (Heeger, Vis Neurosci, 1992).•Simplify read-out, thinking of population code as a probability
density (Simoncelli & Heeger, Vis Res, 1998; Simoncelli, in The Visual Neurosciences, 2003; Beck, Latham & Pouget, J Neurosci, 2011).
• Invariance w.r.t. one or more stimulus dimensions, e.g., contrast, odorant concentration (Heeger, Vis Neurosci, 1992; Heeger, Simoncelli & Movshon, PNAS, 1996; Simoncelli & Heeger, Vis Res, 1998; Ringach, Vis Res, 2009; Olsen, Bhandawat & Wilson, Neuron, 2010).
•Averaging vs. winner-take-all (Busse, Wade & Carandini, Neuron, 2009).•Decorrelation & statistical independence (Schwartz & Simoncelli, Nat
Neurosci, 2001; Lyu & Simoncelli, Neural Comput, 2009; Olsen, Bhandawat & Wilson, Neuron, 2010; Lyu, Axel & Abbott, PNAS, 2010).
Possible circuits & mechanisms
•Might be feedforward, feedback, or a combination of the two (Heeger, J Neurophysiol, 1993)
•Shunting inhibition (Carandini & Heeger, Science, 1994; Carandini, Heeger & Movshon, J Neurosci, 1997)
•Synaptic depression (Carandini, Heeger & Senn, J Neurosci, 2002)• Presynaptic inhibition (Olsen & Wilson, Nature 2008)•Balanced amplification (Murphy & Miller, Neuron, 2009)•Background synaptic activity (Chance, Abbott & Reyes, Neuron, 2002)•Saturation of the inputs combined with spike threshold and
spike-rate rectification (Priebe & Ferster, Neuron, 2008)
•Etc.
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From circuits & mechanisms to behavior
Computation
Circuits & cellular/molecular mechanisms Behavior
Carandini, Nat Neurosci (2012)
Mechanism?
Canonical computation deficit hypothesis
Possible dysfunction of normalization underlying schizophrenia, epilepsy, and other developmental and neurological disorders.
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Schizophrenia: a dysfunction of normalization?
Dakin, Carlin & Hemsley, Curr Biol, 2005
Possible mechanism for normalization deficit
MR spectroscopy
Yoon et al, J Neurosci, 2010