Krubitzer & Kaas
S1
S2
V1
V2
A1
MT
30 μm
pia
white matter
Mouse
Rat
Cat
Monkey
Man
Motor
109.2 ± 6.7
108.2 ±5.8
103.9 ±7.6
110.2 ±9.4
102.3 ±9.5
mean ± s.d.
Somatosensory
111.9 ±6.9
107.0 ±6.7
106.6 ±7.2
109.4 ±9.4
103.7 ±5.8
Frontal
110.8 ±7.1
104.3 ±7.2
108.0 ±6.2
112.0 ±11.1
103.3 ±8.6
Temporal
110.5 ±6.5
107.7 ±9.2
113.8 ±7.3
109.8 ±10.3
107.7 ±7.5
Parietal
104.7 ±7.2
105.2 ±6.8
110.6 ±7.4
114.6 ±9.9
104.1 ±12.5
Visual
112.2 ±6.0
107.8 ±7.9
109.8 ±9.9
267.9 ±13.7
258.9 ±15.8
Mean of
means
109.9 ±6.8
106.7 ±7.4
108.8 ±7.7
-------
Rockel AJ, Hiorns RW & Powell TP (1980) “The basic uniformity in structure of
the neocortex,” Brain 103:221-44.
receptive fields
1
0
1
2
3 mm
Hubel & Wiesel 1974
cortex
visual field
45º
22º
.
0º
Hubel 1982
7º
10º
45º
2 mm
Hubel & Wiesel
“Hypercolumn”
~2 mm
~2 mm
after Hubel & Wiesel 1962
Re-routing experiments (ferret)
visual
lab of Mriganka Sur
auditory
5 mm
1 mm
Roe et al. 1990
Sur et al. 1988
10,000
porpoise
modern
human
Brain weight (grams)
1,000
blue
whale
elephant
E = 0.07  P2/3
100
crow
alligator
10
1 hummingbird
0.1
0.001
Primates
Bony Fish
Mammals
Reptiles
Birds
eel
goldfish
0.01
0.1
1
10
100
1,000
10,000
100,000
Body weight (Kilograms)
Crile & Quiring
Van Essen et al. 1984
2º
1 cm
Tootell et al. 1982
Half of area V1 represents the central 10º (2% of the visual field)
?
Krubitzer & Kaas
S1
S2
V1
V2
A1
MT
Lateral view of monkey brain
Medial view of monkey brain
Felleman and Van Essen 1991
Cortex unfolded
"Thus the hypothesis is that the cerebral cortex confers skill in
deriving useful knowledge about the material and social world
from the uncertain evidence of our senses, it stores this
knowledge, and gives access to it when required."
Barlow 1994
Finding New Associations in Sensory Data
1. Remove evidence of associations you
already know about . . .
. . . to facilitate detecting new ones.
(1/f2 and center-surround)
2. Make available the probabilities of the
features currently present . . .
. . . to determine chance expectations.
(-logp, adaptation)
3. Choose features that occur independently
of each other in the normal environment . . .
. . . to determine chance expectations
or combinations of them.
(lateral inhibition)
4. Choose “suspicious coincidences” as
features . . .
. . . to reduce redundancy and ensure
appropriate generalization.
(orientation selectivity)
Barlow 1994
Context:
Stored knowledge
about environment
Previous sense data
Task priorities
Unsatisfied appetites
Model of
current scene
New associative
knowledge
What we
actually
see
Sensory
messages
Compare
and remove
matches
New information
about environment
This cycle can be repeated
Barlow 1994, fig. 1.3
Schematic of a Kalman Filter
Measurement Update (“Correct”)
Time Update (“Predict”)
(1)
(2)

and P
k 1
k 1
Initial estimates for x
Welch & Bishop, fig. 1.2
(3)
1
Update estimate with measurement zk



x  x   K  zk  Hx  
k
k
k
k
Project the error covariance ahead
P   AP
AT  Q
k
k 1
Compute the Kalman gain
K  P  H T  HP  H T  R 
k
k
 k

Project the state ahead


x   Ax
 Bu
k
k 1
k 1
(2)
(1)
Update the error covariance
P  1  K H  P 
k 
k  k
Neighboring pixels tend to have similar values
Simoncelli & Olshausen 2001
Neighboring pixels tend to have similar values
natural image
1/f 2
Simoncelli & Olshausen 2001
“Whitened”: 2G or what ctr-sur does
Sophie in the Arctic
natural image
1/f 2
whitened image
barlow_filt3.m
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
Reward?
Yes
Yes
Yellow
Volkswagen?
No
Harris 1980
No
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
“yellow
Volkswagen”
cell
dense
YV
“combinatorial explosion”
Harris 1980
“red
Ferrari”
cell
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
“yellow”
cell
dense
Y
V
Harris 1980
“Volkswagen”
cell
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
Yes
Yellow?
No
Harris 1980
Reward?
Reward?
Yes
Yes
No
Yes
Volkswagen?
No
No
Finding New Associations in Sensory Data
(The yellow Volkswagen problem)
sparse
dense
n
k
e
g
“y”
cell
s
y
“v”
cell
v
o
l
a
w
Harris 1980
Y
V
The curve shows how statistical efficiency for detecting associations with a feature X varies with the
value of a parameter defined as follows:
“sparseness”
x=xpxZ / 
where x ,  are the activity ratio for feature X and the average activity ratio, px is the probability of
X, and Z is the number of neurons in the subset under consideration. For instance, one could
identify an association with any one of the 45 possible pairs of active neurons in a subset of 10 with
an efficiency of 50% provided that the neurons were active independently, the pair caused two
neurons to be active, the probability of the pair occurring was 0.1, and the average fraction active
was 0.2. (From Gardner-Medwin and Barlow 1994)
Gardner-Medwin & Barlow 2001
What are the desirable properties of
directly represented features?
“. . . primitive conjunctions of active elements that
actually occur often, but would be expected to occur
only infrequently by chance,” that is,
“suspicious coincidences”
Gardner-Medwin & Barlow 2001
“Whitened”: 2G or what ctr-sur does
Sophie in the Arctic
Suspicious Coincidences
6
log10(#)
Random
4
2
0
2
3
4
5
6
7
8
log10(#)
6
Line
4
p < 0.0100
2
0
2
3
4
5
6
7
8
sum of 9 pixels
barlow_filt3.m
The perfect map?
A more useful map
11
12
13
K
L
T
T
M
Streets
Aberdeen Rd …….….C7
Academy St …….…...D9
Acorn Pk ……….…....F9
Acton St ……….…….C7
Adamian Pk …....……C9
Adams St ……….…...D9
Addison St ……..……D9
Aerial St ……….…....C8
Albermarle St ….……D8
Alfred Rd …………....E9
Allen St ……………...D9
Alpine St ………...…..C7
.
.
.
.
.
.
.
.
.
.
.
.
.
Longwood Ave …….L12
MBTA map
Linking Features: Orientation
Guzmann 1968
Striate cortex contains a map of
orientation.
“Hypercolumn”
after Hubel & Wiesel 1962
“Space”
Tootell et al. 1982
“Feature”
Bosking et al. 1997
Tootell et al. 1982
Linking Features: Orientation
Guzmann 1968
hierarchy
gain adjustment
(1024 * 768)pixels * 24 bits/pixel = 18,874,368 bits
edge detection
invariance
a) position
b) sign of contrast
curvature
38 points * 2 words/point * 16 bits/word = 1,216 bits
compression ratio = 15,522
Takahashi, Nowakowski & Caviness 1996
Q1
Q1
+
(P12)Q2
Cumulative
Output
Q1
+
(P12)Q2
+
(((P12)P2)2)Q3
(((P12)P2)2)Q3
(P12)Q2
mitosis
Q1
PVE Size
1
P1
P12
CC #1
Takahashi, Nowakowski & Caviness 1996
(P12)P2
CC #2
((P12)P2)2
(((P12)P2)2)P3
CC #3
neuronogenetic.m
150
1
PVE volume
#
0.8
Q
PVE output
Cumulative output
100
0.6
0.4
50
0.2
0
0
1
2
3
4
5
6
7
8
9
10 11
Elapsed Cell Cycles
E11
E12
E13
E14
E15
0
0
2
4
6
8
10
Elapsed Cell Cycles
E16
Takahashi, Nowakowski & Caviness 1996
E17
12
1 mm
2 mm
Chenn & Walsh 2002
Grove & Fukuchi-Shimogori 2003
Fukuchi-Shimogori & Grove 2001
gain of function
(S1 smaller and
shifted rostral and
lateral)
loss of function
(S1 larger and
shifted caudal and
medial)
Hamasaki et al. 2004