Biological
Cybernetics
Biol. Cybernetics26, 45-52 (1977)
@ by Springer-Verlag 1977
A Model of Visual Development
T. Nagano
InformationSciencesDivision,ElectrotechnicalLaboratory,Tokyo,Japan
Abstract. There is now abundant evidence that the
structure o f the mammalian visual cortex is not innately
determined but can be altered by visual experiences
during a certain period at an early age. A model based
on the evidence is proposed that will explain some
aspects of the developmental process in the visual
cortex. The model self-organizingly forms "a simple
cell" which responds to bars and edges of a certain
orientation and retinal position. The total system o f the
model corresponds to "a hyper column" which contains
a complete cycle of orientational selectivity. The model
has the following three original points, i) "A hyper
column" is finally formed in the model, ii) Most of the
cells do not have orientation selectivity in the initial
state, iii) It is hypothesized that the orientation continuity of the hyper column is caused by similar
orientations of successive input stimuli. The results of
computer simulation show that the model has the
expected performance.
1. Introduction
Neurophysiological studies on the mammalian visual
system have been steadily progressing since Hubel's and
Wiesel's works (1962, 1963a). Many nervous network
models of the visual system based on these studies have
also been reported (e.g., Deutsch, 1966; Hiwatashi and
Osada, 1967; Fukushima, 1969). Hubel and Wiesel
(1963a) found cells responding selectively to bars or
edges of a certain orientation in striate cortex of very
young, visually inexperienced kittens. They concluded
that the nervous networks detecting bars or edges were
innately determined. This notion has been adopted in
modeling of the nervous system of the brain. That is,
basic features of input patterns are assumed to be first
extracted by ad hoc networks with innately determined
structures, and then higher-order information processings, such as concept formation by integrating the
extracted features, relating concepts with each other
and so on, are made by nervous networks organizable
according to experiences after birth (Mart, 1969;
Fukushima, 1973; Nagano, 1974).
But several neurophysiological findings against this
Hubel's and Wiesel's conjecture have recently been
reported. They show that the visual feature extraction
mechanism will also be organized according to experiences after birth (Hirsch and Spinelli, 1970;
Blakemore and Cooper, 1970 ; Pettigrew and Freeman,
1973; Blakemore and Van Sluyters, 1975; Barlow,
1975). A model of visual development based on these
findings are proposed in this paper. The model is
simulated on a digital computer to confirm its performance.
2. Visual Development and Columnar Organization
Hubel and Wiesel (1963a) showed the results that
responses of neurons in the visual cortex of visually
inexperienced kittens were very similar to those of
adults. They concluded that feature extraction networks of the visual cortex were innately determined.
But recently several findings against their conclusion
are reported. Hirsch and Spinelli (1970) investigated the
visual cortex of kittens that were raised from birth with
one eye viewing horizontal lines and one eye viewing
vertical lines. They found that elongated receptive fields
of cells in the visual cortex were horizontally or
vertically oriented. No oblique fields were found.
Moreover, cells with horizontal receptive fields were
activated only by the eye exposed to horizontal lines;
cells with vertical receptive fields only by the eye
exposed to vertical lines. Blakemore and Cooper (1970)
reported similar results. Pettigrew and Freeman (1973)
found that cells in the visual cortex of kittens raised
from birth in an environment consisting entirely of
small spots of a certain size responded best to the spots
46
+'-kkttlt+
--.-',,
',, f / / . - ' -
--.--...',,\ttt...'----'----\ k t t t --'--Fig. 1. Orientation selectivityof E-cellsin a hyper column. Each bar
indicates the optimal orientation of a given E-cell
. . \,,,k
dimensions. The model proposed here deals only with
the simple cell as is so in all the other models of visual
development. Only the orientation selectivity of cells is
considered and ocular dominance of cells is not taken
into account to simplify the model.
3. Review of Visual Developmental Models
Models of visual development proposed till now are
summarized in order to clarify the differences between
them and the model proposed here.
/ #-.-
'"
Von der Malsburg's Model (1973)
"--" / t " - " - "
t t \ ' , .
9
" " t/
9
#
"~'~,-~,,~
Fig. 2. View onto the cortex after 100 steps of learning. Each bar
indicates the optimal orientationo f a givenoutput cell. Dots without
a bar are cellswhichnever reactedto the standard set of stimuli (yon
der Malsburg, 1973)
with the same size. It is certain from these findings that
visual experiences during a certain period at an early
age change the visual nervous system. A finding
supporting this notion has also been reported in the
study of binocular vision (Wiesel and Hubel, 1963).
It is well known that the neocortex consists of an
array of columns each of which corresponds to some
functional unit (Lorente de No, 1938). In the visual
cortex each column consists of cells responding selectively to lines and edges of a certain orientation, and
neighboring columns have similar orientation selectivity (Hubel and Wiesel, 1963b, 1968). Recent Hubel's
and Wiesel's works (1974a, 1974b) show that the visual
cortex has a higher-order functional unit called hypercolumn. A hypercolumn is, the area of cortex about 1 or
2 mm square, within which a complete cycle of ocular
dominance is contained when moving across the cortex
in one direction, and a complete cycle of orientational
selectivity when moving in the orthogonal direction (see
Fig. 1). Hyper columns are arranged like a mosaic on
the cortex.
As is generally known, the visual cortex has roughly
three types of cells : the simple cell responding to lines
and edges of a certain orientation and retinal position,
the complex cell responding to lines and edges of a
certain orientation on a wide area of the retina, and the
hyper complex cell responding selectively to bars or
edges with particular orientations and various critical
His model is composed of the uniform two dimensional
array of pairs of an excitatory cell (E-cell) and an
inhibitory cell (I-cell). Each afferent input fiber connects only to E-cells via excitatory modifiable synapses.
All the connections between cells in the cortex are made
with fixed synapses. Each E-cell connects to other Ecells in its surrounding region of a certain size. Each Icell connects to E-cells in its surrounding region of a
larger size than that of the E-cell's region. No connections are assumed between/-cells. Initial values of
synaptic efficacies between input fibers and E-cells are
random. Each synapse changes its efficacy only when
the post synaptic E-cell is active. It increases its efficacy
when its input fiber is active and decreases its efficacy
otherwise. Synaptic efficacies of each E-cell are normalized to keep the summation of synaptic efficacies
constant whenever efficacies are modified. Each E-cell
is organized to respond to lines of paticular orientation
by the iterative presentation of lines with various
orientations. Figure 2 is a result of computer simulation. It shows that this model well simulates the
formation of columnar organization since the E-cells
with the same orientation selectivity form a cluster.
Nass's and Cooper's Model (1975)
Their model is similar to yon der Malsburg's one except
that their model lacks connections between E-cells. A
model with/-cells is compared with a model without Icells. It is shown that/-cells are necessary for E-cells to
be organized to have orientation selectivity. The constancy of the summation of synaptic efficacies is not
assumed because of its improbability in the actual
nervous systems. Instead of the restriction, the decay of
each efficacy proportional to its value is introduced
throughout the learning period to produce similar
learning effect without the restriction. It is shown that
the concentric receptive field organization of lateral
geniculate cells makes the output of an E-cell minimum
when input bars are a little rotated fl'om its optimum
47
orientation. They propose that this effect may provide a
cue signal for neighboring columns to be organized to
have similar orientation.
Hall's and Yau' s M o d i f i c a t i o n A l g o r i t h m (1976)
o|174
%o|
9
The way of modifying efficacies (modification algorithm) to produce orientation selectivity is studied
mathematically. In order to organize E-cells to have
orientation selectivity without lateral inhibition by Icells, two types of modification algorithms are necessary: one is Hebb's way that increases synaptic
efficacy only when simultaneous excitation of pre- and
post synaptic cells occurs and otherwise decreases it
gradually; the other is the way similar to that used in
vonder Malsburg's model except the restriction that the
summation of efficacies is constant. The former way is
necessary at the early stage of learning and the latter at
the later stage of learning.
Grossberg (1976) also has proposed a model of
visual development. A lateral inhibition mechanism
other than Nass's and Cooper's one is proposed in his
model. It enables his model to detect only relative
intensities of inputs. The restriction that the summation
of efficacies is constant can be eliminated by using
relative intensities of inputs as input signals.
4. Description of the Model
Three original points of the model are first described.
i) Almost all the cells have no orientation selectivity
in the initial state.
ii) A hyper column shown in Figure 1 is formed.
iii) The formation process of a hyper column
depends on input pattern sequence.
The review of neurophysiological findings in 2
shows that cells of young visually inexperienced kittens
will have weak orientation selectivity and that their
"tuning" characteristics will be improved by visual
experiences after birth. It may, therefore, be accepted
that E-cells of a model have weak orientation selectivity
in its initial state as in yon der Malsburg's model. But a
model with such an initial structure is not interesting
because it is easy to devise such a model that is
composed of E-cells with innately determined orientation selectivity and that only tuning characteristics of
E-cells are improved by visual experiences. Almost all
the E-cells of the model proposed here are, therefore,
assumed to have no orientation selectivity in its initial
state. Only a very few E-cells have weak orientation
selectivity in order to trigger the model because the
model could not begin to form orientation selective
cells if no cells had orientation selectivity.
9
9
%%...%
Fig.3. Arrayof cellsin the presentmodel. 9and @are an E-celland an
/-cell, respectively
All the previous models reviewed in 3 simulate only
the formation of the columnar organization and the
improvement of orientation selectivity. None of them
do not simulate the hyper columnar organization in
Figure 1.
As was previously described, Nass and Cooper
considered that a large falling-off of E-cell's output
caused by the concentric receptive field organization of
lateral geniculate cells might become a cue signal for
neighboring columns to be organized to have similar
orientation selectivity. According to their thought, the
orientation difference between two neighboring columns becomes about 20 ~. But the difference in the
actual cortex is far smaller, [e.g., 7.2~
~ in the
monkey striate cortex; Hubel and Wiesel (1974a)]. It
does not, therefore, seem that the actual cortex uses
such a cue signal. The continuity of columnar organization is assumed to be caused by continuous changes
of input orientation in the model proposed here. The
adequency of this hypothesis is as follows. Newborn
animals seem to look their environments around uncouciously without gazing some paticular things intentionally. Their heads and bodies seem to move
slowly and continuously. It is, therefore, quite natural
to think that input bars and edges are presented to the
retina with continuous changes of their orientations. It
also supports this hypothesis that cells with each
orientation selectivity are equally dense in spite of the
predominant majority of vertical and horizontal lines
to oblique ones in the actual environments.
The structure of the model is described in the
following. The model is composed of M x N two
dimensional array of pairs of an E-cell and an/-cell as is
shown in Figure 3. Each E-cell is the output cell of the
cortex and/-cells are interneurons. Input signals from
the lateral geniculate cells are denoted by
X =(Xl, x2,..., xL),
where o < x t < Xmax(l = 1, 2 , . . . , L).
(1)
48
Xl
X 2
X3
9
9 ,
Table 1. Notations of synaptic efficacies
XL
Connection
Synaptic efficacy
xl-~ E-cell
E-cell~ E-cell
E-cell--,I-cell
/-cell-~ E-cell
wz.ij(1 = 1, 2 , . . . L ; i
= 1, 2 , . . . M ;j = 1, 2 , . . . N )
amj, u(m + i; m, i = 1, 2, ...M ;j = 1, 2,...N)
b,~j. u(m, i = 1, 2, . . . M ;j = 1, 2 , . . . N )
c,,,, u(m, i = 1, 2, .. . M ; n ~ j ; n,j = 1, 2, . ..N)
Fig. 4. Connection between input fibers and an E-cell. ~ indicates
an excitatory modifiable synapse. Every input fiber connects to each
E-cell via an excitatory modifiable synapse
O
O
&
0
O
(30
0
0
Fig. 5. Connection between E-cells. --<3 indicates a excitatory fixed
synapse. Each E-cell connects to the other E-cells in the same column
C)
0
Fig. 6. Connections between E-cells and an/-cell. ~ O indicates an
inhibitory fixed synapse. Each E-cell receives inputs only from all the
E-cells in the same column via excitatory fixed synapses. Each/-cell
connects to the E-cells in the other columns via inhibitory fixed
synapses
Every input fiber connects to each E-cell via an
excitatory modifiable synapse (Fig. 4). No input fibers
connect to/-cells directly. Connections between E-cells
are shown in Figure 5. Only E-cells in the same vertical
column of the array are connected with each other via
excitatory fixed synapses. Figure 6 shows connections
between E-cells and an/-cell. All the E-cells in the same
column connect to each /-cell in that column via
excitatory fixed synapses. Each /-cell connects to Ecells in all the other columns via inhibitory fixed
synapses, though Figure 6 shows only connections
between neighboring columns for simplicity. Synaptic
efficacies of connections between neighboring columns
have to be maximum. No connections are assumed
between/-cells.
Input output relations of the two types of cells are
described. The summation of all the weighted inputs of
a cell is called the "potential" of the cell. Potentials of Ecells and /-cells are denoted by yij(t) and zu(t ) (i = 1,
2,..., M ; j = 1, 2,..., N), respectively, where t is time.
Output of E-cells and/-cells are denoted by y*(t) and
z*(t), respectively. The relation between a potential and
an output is given by Figure 7. Notations Ymax,*Zmax,*0y,
0z, Ys, and zs are easily understood from this figure. All
these parameters are assumed to be independent of i, j.
Notations of synaptic efficacies are defined in Table 1.
Potentials and outputs of the E-cells and the/-cells are
given by the following equations.
L
M
y,j(O = Y~ w~,,j(Oxz(O+ ~ amj,iy*~(t-- t)
l=1
m=l
m*i
M
-
Z
N
Z cm.,uz*.(t- lt,
(2)
ra=l n = l
n~j
y orz
(3)
y*(t) = Oy(yu(t)) ,
(4)
z~(t) =o~(zij(t)) ,
(5)
m=l
Yrnax
or
Z~
rnox
0
M
Zij(t)= E bmj, iJYmj(t),
@ o r 8z
y~ orz~
y orz
Fig. 7. Input-output relations of an E-cell and an/-cell
where Oy and O~ are the analog threshold functions
defined by Figure 7.
The modification of synaptic efficacy is assumed to
occur only when the potential of an E-cell exceeds the
modification threshold d, where d is greater than the
output threshold 0r The modification equation in this
49
model is given by
wl, ij(t) = wt, ij(t - 1) + k 1xt( t - 1)y~:( t - 1)
XI(I.- 1))y/*j(t- 1),
--]s
(6)
where y~j(t) is defined by
y[j(t) = y i i ( t ) - d ,
= 0,
if
y,j(t)>d
otherwise,
(7)
k~ >0, k 2 > 0 and 0<Wl,~j_--<Wma~.
This modification algorithm is similar to the second
one in Hall's and Yau's work except the existence of
the modification threshold which is greater than the
output threshold 0y.
5. Initial Conditions and Principles of Behavior
Three assumptions are made for simplification.
i) x t = 1 or 0, (1= 1, 2, ..., L).
ii) IXl = K = const, where IXl means the number of
components whose values are 1.
iii) Each/-cell connects only to E-cells in the two
neighboring columns.
In order to satisfy the condition that ahnost all the
cells have no orientation selectivity in the initial state,
synaptic efficacies amj,~i, b~j,~j, and cm;+t,ij are made
independent of m, i, andj. These constant efficacies are
expressed by a, b, and c, respectively. Almost all the
modifiable synaptic efficacies have the same initial
value Wo(0< w o < W~a~). The rest (which are very few)
have a value w o + A w o ( A w o >0). As the formation of
orientation selectivity is caused by the differences of the
potentials between E-cells, the model could not start if
all the E-celIs had an equal potential. A very few
synaptic efficacies are, therefore, given a greater initial
value than others to produce a small potential difference which triggers the model. The initial values of
synaptic efficacies make almost all the E-cells have
equal potential to every input pattern (a bar or an edge).
A very few E-cells with the synaptic efficacy w o + A w o
have a different potential when the synapse receives an
active input signal.
The following roughly explains how a hyper column
is formed from these initial conditions. An E-cell having
a synapse with efficacy w o + A w o is denoted by E 0. An
input pattern supplying an active signal to the synapse
is denoted by X o. The potential of E o is higher than
other E-cells by A w o when X 0 is presented. This
potential difference causes the change of synaptic
efficacies of E o according to (7) so as to produce the
selectivity to X o. The potential difference is transmitted
to other E-cells in the same column of the array via
colateral fibers in Figure 5, resulting in the formation of
the same orientation selectivity for the E-cells. As is
understood from (7), the E-cells organized to have the
selectivity to X o have lower potential than the initial
potential for any other input pattern with different
orientation. This falling-off of potentials is transmitted
to the E-cells in the neighboring columns v i a / - c e l l s in
Figure 6, resulting in the increase of the potentials of the
E-cells in the neighboring columns. The synaptic efficacies of these E-cells are, therefore, modified so that
the E-cells may have the selectivity to the input pattern
X 1 following X o. Consequently a hyper column is
formed if the orientation of input patterns change
gradually and continuously.
Conditions for a hyper column to be formed is
derived in the following. It is necessary that the
potential change of each cell causes the change of its
output in the initial state, The initial potentials yi~(0),
zij(0), therefore, have to satisfy
0y < y,.j(0)< Ys,
0~ < z~j(0)< z s .
(8)
In order for the model to be triggered only by the
input to the synapse with the efficacy w o + A w o , the
potentials of all the E-cells are lower than the modification threshold d when such synapses are not activated. In such a case, y~(0) and z~j(0) are independent of
ij and are denoted Yo and zo, respectively. From (2) and
(3), Yo and z o are given by
Yo = K w o + ( M -
1)avy(yo - Oy)
- 2mcTz(Zo - Oz),
z o = M b T , ( y o - 0,),
(9)
(10)
where 7y and 7z are the gradients of the linear parts of
the relations in Figure 7. Hence we have
Yo =
K w o - ( M - l)aTy0y + 2M2bcyyTzO~, + 2 M c ~ O ~ < d.
1 - (M - 1)avy + 2M2bcTy7z
(11)
The condition for the synaptic efficacies of E o to be
modified by the presentation o f X 0 in the initial state is
given by
yo + A w o > d .
(12)
During the presentation of each input pattern, h times
of modifications are assumed to be made. Let 5w+ and
cSw_ be, respectively, the increase and the decrease of
synaptic efficacies of E o caused by X o. Ignoring the
effect that the potential change of E o is fed back to E o
via other E-cells by assuming a, b, c ~ 1, we have
c%v+ = kick(1 + k l K ) h- 1,
(13)
~w_ = -- k2~(1 + kaK) h- 1,
(14)
where
c~=yo + A wo - d.
(15)
50
TINES OF ITERATION
0000000000Q
00000000000000
0000
0 0 0 0 0 O0
00000000000000
00000
000000
1
2
3
4
=
5
0 00
TIMES OF ITERATION
12300000000032
12300000000032
12300000000032
12300000000032
12300000000032
TIMES OF ITERATION = 2
0 0 00 0 0 0 0 0 00 0 00
0000
00000000
O0
00000
00 00 O 0 0 0 0
00000000000000
00 00 0 0 0 00 00 0 00
TINES OF ITERATION
12345600065432
12345600065432
12345600065432
12345600065432
12345600065432
-
6
TIMES OF ITERATION = 3
10000000000000
000000000
O0 0 0 0
00000
000000
000
00000000000000
0000
0000
000000
TIMES OF ITERATION
12345670765432
12345670765432
12345670765432
12345670765432
12345670765432
=
7
TIMES OF ITERATION
=
8
TIMES OF ITERATION
: 1
000
0 00
:
4
12000000000002
5
6
7
8
Fig. 8. Straight line segments used as input patterns in the computer
simulation
TINES OF ITERATION
00000000000000
00000000000000
00000000000000
00000000000000
00000000000000
=
1
TIMES OF ITERATION
I0000000000000
00000000000000
00000000000000
00000000000000
00000000000000
:
2
TIMES OF ITERATION
12300000000032
12300000000032
12300000000032
12300000000032
12300000000032
=
3
TIMES OF ITERATION
12345600065432
12345600065432
12345600065432
12345600065432
12345600065432
=
4
TIMES OF ITERATION
=
5
12000000000002
12000000000002
12000000000002
70 765432
781765432
781765432
2345678[765432
Fig. 12. Formation process of a hyper column in the case of partially
irregular input sequence. The numerals and the square in this figure
have the same meanings as those in Figure 9
The condition for the potentials o f the E-cells in the
same c o l u m n as E o to exceed the modification threshold on the presentation of X o is given by
Yo +
a?y(Awo+ K6w +)> d.
(16)
The number o f input fibers which are activated by
both X o and X 1 is denoted by f. The condition for the
potentials o f the E-cells in the neighboring columns to
exceed the modification threshold on the presentation
of X 1 is given by
yo-C?~{bTy(f6w+ + ( K - f ) 6 w +Awo) } > d .
7 ~ 7 6 5 4 3 2
7~765432
234567~765432
Fig. 9. Formation process of a hyper column in the case of systematic
input sequence. The part enclosed by a square is a hyper column. The
numerals in this figure indicate each orientation of input patterns (see
Fig. 8). The numeral 0 means that the potential of a given E-cell is not
high enough for any one of the input patterns
(17)
We can assume f ~ K since X o and X 1 are straight
line segments with different orientation. The second
term of the left side of (17) can, therefore, b e c o m e
positive so that (17) m a y be satisfied, i f k 1 and k 2 are not
so m u c h different.
6. Computer Simulation
POTENTIAL DISTRIBUTION
1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 0 . 6 0 3 . 4 0 2 . 7 0 9,91
1 . 0 0 1 . 0 0 1 . 0 0 l . O0 0.60 3.40 2.70 9.91
1.00 1.00 1.00 1.00 0.60 3.40 2.10 9.91
1 . 0 0 1 . 0 0 1 . 0 0 1 . 0 0 0 . 6 0 3 , 4 0 2.70 9.91
1.001,001.001,000.603.402.709.91
2 . 7 0 3 . 4 0 0 . 6 0 l . O01.001.00
2.703.400.601.001.001.00
2.70 3.40 0.60 1.00 1,00 1.00
2.70 3 . 4 0 0 . 6 0 1 . 0 0 1 . 0 0 1 . 0 0
2.703.400.601.001.001.00
Fig. 10. Potential distribution for the pattern No. 8 after five times of
interation
WEIGHT OISTRIBUTION
0.
0.
O.
O.
1.000
O.
O.
O.
O.
O.
O. :
O.
1.000
O.
O.
O.
O.
O.
Q.
O.
1.000
O.
O.
0.
O.
Oo
O.
O.
1.000
O.
O.
O.
O.
O.
O.
O.
1.000
0.
O.
O.
O.
O.
O.
O.
1.000
O.
O.
O.
O.
O.
O.
O.
1.000
O.
O.
O.
O.
0.
O.
O.
O.
O.
O.
O.
O.
O.
O.
1.000
O.
0.
O.
O.
O.
O.
O.
O.
I,000
O.
O,
O.
O.
Fig. 11. Final synaptic efficacies of an E-cell responding selectively to
the pattern No. l
Eight straight line segments with different orientations
shown in Figure 8 were used as input patterns. Black
meshes and white meshes of each pattern are assumed
to express active inputs (1) and silent ones (0), respectively. The array of cells are 5 x 14, that is, M = 5
and N = 14. The first c o l u m n and the 14-th column are
connected with the same way as other neighboring
columns in order to m a k e the structure of a small-scale
m o d e l uniform. Specific values o f other parameters are
amj, ij = 0.1(m @ i;j= 1, 2, ..., 14; m, i = 1, 2, ..., 5)
b,,j,u = 0.1(j = 1, 2 , ..., 14; re, i = 1, 2, ...,5)
%-, u = 0.08(n = j + 1 ;j = 1, 2 , . . . , 14 ; m, i = 1, 2 . . . . . 5)
wl, q(0) = 0.5(/= 1, 2 . . . . . 81 ;j = 1, 2 . . . . , 1 4 ; i = 1, 2,..., 5)
51
with the exception that
w37' it(0) = 1.0,
Oy = 0 z = 0 . 0 ;
d=4.5 ;
Y~ = Zs = ~
kl =k2=0.1 ;
;
7y = ~ = 1 . 0 ;
Wmax=Xmax=l.0.
Input patterns were iteratively presented in order
according to the numbers of the patterns in Figure 8 to
satisfy the hypothesis about the way of input pattern
presentation. Figure 9 shows the numbers of the
patterns which are selected by each E-cell. A hyper
column (a part enclosed by a square in this figure) is
formed after five times of iteration. Figure 10 shows the
potential of each E-cell caused by the pattern No. 8
after learning. Figure 11 shows the final synaptic
efficacies of an E-cell responding selectively to the
pattern No. 1. Both figures show that the model has the
expected performance.
Each pattern was presented completely in order in
the above simulation experiments so that the orientation of input patterns may change continuously from
0 ~ to 180 ~ But large and distrete changes of orientations seem to occur sometimes on the actual retina of
newborn animals. The performance of the model to
such an input sequence was also investigated. The input
sequence in this case was composed of the iteration of a
cycle 123456, 345678, 567812, 781234. Figure 12 shows
the result that the formation of a hyper column was
successful even when input sequence contained sudden
changes of orientations.
7. Discussion
The following three facts are known about the neocortex: the number of the principal neuron (E-cell) is
roughly equal to that of the interneuron (/-cell); there
exsist inhibitory interneurons; axon colaterals of a
principal neuron are connected to other principal
neurons. Though the way ofaxon branching is not clear
about inhibitory interneurons of the neocortex, inhibitory interneurons in the other parts of the brain
(e.g., the cerebellar cortex and the hippocampus) extend
their axon branches only to a particular direction. The
structure o f the model does not conflict with these facts.
One of the original points of this research is the
hypothesis that the continuity of the columnar organization is caused by the continuous change of the
orientation of input patterns. The continuity of the
columnar organization does not seem to be indispensable for further in formation processing after the extraction of line segments. On the other hand, it is very
difficult to devise a model which realize the continuous
columnar organization regardless of input pattern
sequences. Such a model seems to have a structure with
great complexity caused only by the realization of the
continuity. Such an unbalance of the little necessity
and the great complexity does not seem to exist in living
organisms since they are considered to be reasonably
organized by the natural selection. This is the reason
why the continuous columnar organization is assumed
to be formed simply by the continuity of the orientation. As this hypothesis can be examined by neurophysiological experiments, this model can be said to
offer a research theme to experimental neurophysiologists.
Acknowledgements. The author thanks to Mr. T. Hamada and Dr. B.
Furubayashi of Electrotechnical Laboratory for their helpful discussions.
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Received: November 25, 1976
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