![Page 1: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/1.jpg)
Attributes of a neural code for perceptual/cognitive computation
Presented Feb 12, 2003Mathematical Biosciences Institute
Ohio State University
David W. Arathorn
Copyright(c)2003 David W. Arathorn
![Page 2: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/2.jpg)
Unless otherwise indicated all diagrams from
“Map-Seeking Circuits in Visual Cognition”
David W. ArathornStanford University Press
![Page 3: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/3.jpg)
M ap-S eek in g C ircu its In V isu al C ogn ition
David W . A ra thorn
from Stanford University Press
![Page 4: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/4.jpg)
A neural code must be able to support a
sufficiently rich computational repertoire
![Page 5: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/5.jpg)
• It must encode a sufficient range of values with sufficient accuracy and discriminability
• It must close under a sufficient set of operations implementable with neural mechanics
![Page 6: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/6.jpg)
Two alternative approaches to problem, not mutually exclusive
• Try to deduce the code from inputs
• Try to deduce the code, or at least specific characteristics of the code, from computational requirements
![Page 7: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/7.jpg)
Starting with the second approach
• What are the operations necessary to support a realistically complex computation?
![Page 8: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/8.jpg)
– combine, – match, – map, inverse map, – compete, – attenuate, – scale – a nonlinearity (if not inherent)
A circuit composed of the following operations…
is capable of a variety of visual functions, computing inverse kinematics, and other cognitive computations
![Page 9: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/9.jpg)
s s
2
f
w1
g1
g2
g3
q1
q2
q3
b
b
w
m w11
m w22
forward backward
r
f
d1( )r d2( )r d3( )r
i ig d b r
map, attenuate, combine
![Page 10: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/10.jpg)
s s
2
f
w1
g1
g2
g3
q1
q2
q3
b
b
w
m w11
m w22
forward backward
r
f
d1( )r d2( )r d3( )r
k km f b w
k k k
k
m f b w b w w�� attenuate, combine
match, non-linearity
![Page 11: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/11.jpg)
s s
2
f
w1
g1
g2
g3
q1
q2
q3
b
b
w
m w11
m w22
forward backward
r
f
d1( )r d2( )r d3( )r
i iq d b r�
comp , g g q
match, map
competition
![Page 12: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/12.jpg)
Mapping module for multilayer circuits
s
d 1( )r
g 1g 2
g 3
q 1
q 2
q 3
b b
forw ard backw ard
r
s
d 1 ( )b-1
r
d 2 ( )b-1 d 3 ( )b
-1
d 2( )r d 3( )r
![Page 13: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/13.jpg)
FORWARD BACKWARD
input image
layer 1
layer 2
memory
![Page 14: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/14.jpg)
algebraic versions of the basic operations
i ig d b r
k km f b w
k k k k
k k
m f b w b w w��
i iq d b r�
comp , g g q
1) map, attenuate, combine: b forward, b and r backward superpositions
2) match, non-linearity: memory response and forward/backward match
3) competition: mapping coefficient competition
1i ig d r b
��
![Page 15: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/15.jpg)
Role of the Ordering Property
In two places there is a match between a superposition and a pattern (which itself may be a superposition from another layer in multilayer circuits.)
si S s are components of superposition si
r S r is not component of superposition si
Ordering property is
P(sj si > r si ) >> P(sj si < r si )
for sj S
Depends on sparsity of si and number of components of si
![Page 16: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/16.jpg)
s1
s2
sr
Edge-filtered images are sparse high dimensional vectors
During convergence only a small excess needed: sj si > r si
r is composed of parts of various si and is dismantled during convergence
![Page 17: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/17.jpg)
FORWARD BACKWARD
input image
layer 1
layer 2
memory
![Page 18: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/18.jpg)
First, search concurrently for locating patterns anywhere…
Then, search seqentially for confirming feature patternsin locations predicted by head model….
lynx image courtesy U.S Fish and Wildlife Service
iter 1
iter 25
(next slide)
![Page 19: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/19.jpg)
iter 1 iter 20
iter 40
iter 60 iter 80 iters 20+40+60+80
pattern x-loc y-loc orient yscale xscaleeyes 110 69 7.500 0.850 0.850 ------snout 109 48 7.500 0.850 0.800------left ear 83 108 12.500 1.000 0.900------right ear 144 99 27.500 0.900 0.850
![Page 20: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/20.jpg)
Pattern location – related to tracking
antelope image courtesy U.S Fish and Wildlife Service
![Page 21: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/21.jpg)
Training model, 3D normals
![Page 22: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/22.jpg)
Signal encoding has to “interoperate” with plausible synaptic encoding... e.g. encoding of 3D normals
1
2
3
41
2
3
4
00.250.5
0.75
1
1
2
3
4
0
50
100
1500
50
100
150
0
0.5
1
0
50
100
150φ
ψ
k - encode( <ψ,φ>) encode(<90,90>)
16 synapse weights (wi = e -| v-ci | 2 )
per <x,y,z> encode spherical orientation of normal
determine if viewpoint orientation perpendicular to model normal
![Page 23: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/23.jpg)
Input image
0 50 100 150 200
0
50
100
150
200
3d models courtesy www.3Dcafe.com
![Page 24: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/24.jpg)
0 50 100 150 200
0
50
100
150
200
3D projection
rotation in plane
scale/aspect
translation
iter 1 iter 25
![Page 25: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/25.jpg)
25, 0.01, 0.15, 10, F, -10.0, -5.0, 2.5, 1.0, 1.0, 0.05, 1.0, 1.0, 0.05, 0.7, 1.4, 0.1, 1.3, 1.3, 0.1, 1.4, 1.4, 0.1, -75.0, -15.0, 5.0, 10.0, 45.0, 5.0 /1, 1, 25 pig.dat1, 50 / testsamples, interval pig1dis4_h.datpig1dis4_v.datpig1dis4_l.datpig1dis4_r.dat
----------------- 40000 25667929 1 17708 108 111 1.000 2 17709 109 111 0.533
------------------
1 1 25667929 1 2 -5.000 1.000 1.000 1.000 2 1 -7.500 1.000 1.000 0.363------------------
1 1 25667929 1 3 1.000 1.300 1.400 1.000 2 4 1.100 1.300 1.400 0.911 3 2 0.900 1.300 1.400 0.409 4 5 1.200 1.300 1.400 0.283------------------
13 8 25667929 1 67 -35.000 25.000 1.000 2 66 -35.000 20.000 0.823 3 59 -40.000 25.000 0.730 4 65 -35.000 15.000 0.289 5 58 -40.000 20.000 0.137 6 75 -30.000 25.000 0.065
translation
rotation in plane
scaling/aspect
3D projection
![Page 26: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/26.jpg)
another view
25, 0.01, 0.15, 10, F, -30.0, 0.0, 3.0, 1.0, 1.0, 0.05, 1.0, 1.0, 0.05, 0.7, 1.4, 0.1, 1.3, 1.3, 0.1, 1.4, 1.4, 0.1, -75.0, -15.0, 5.0, 10.0, 45.0, 5.0 /1, 1, 25 ------
1 1 25661176 1 8 -6.000 1.000 1.000 1.000 2 7 -9.000 1.000 1.000 0.902 3 9 -3.000 1.000 1.000 0.681 4 10 0.000 1.000 1.000 0.335 5 6 -12.000 1.000 1.000 0.195------
1 1 25661176 1 5 1.200 1.300 1.400 1.000------
13 8 25661176 1 17 -65.000 15.000 1.000 2 27 -60.000 25.000 0.591 3 16 -65.000 10.000 0.526 4 26 -60.000 20.000 0.294
rotation in plane
scaling/aspect
3D projection
iter 1
iter 25
![Page 27: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/27.jpg)
layer 1 layer 2 layer 3
translation rotation scaling/perspect
mapping convergence
iter 1
iter 25
![Page 28: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/28.jpg)
Recharacterization: mappings as data
-10 -5 0 5 10-15
-10
-5
0
5
10
15
-10 -5 0 5 10-15
-10
-5
0
5
10
15
memory pattern 2 components input pattern
locations of activemappings at endof convergence
Concurrently active translational mappings pop out figure defined by repeated pattern.
![Page 29: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/29.jpg)
Another composed inverse mapping problem:inverse kinematics
1
2
3
p0
p3
seg 1
seg 2
seg 3
constr3(F2)
constr2(F1)
![Page 30: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/30.jpg)
Convergence to inverse kinematic solution
0 20 40 60 800
20
40
60
80
0 20 40 60 800
20
40
60
80
0 20 40 60 800
20
40
60
80
10 20 30 40 50 60 70 80
10
20
30
40
50
60
70
80
Layer 3/Segment 3 Layer 2/Segment 2 Layer 1/Segment 1
iter 1
iter 2
iter 5
0 20 40 60 800
20
40
60
80
activate end effector targetlocation
![Page 31: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/31.jpg)
Can the basic operations be implemented with neural or other analog mechanisms?
– combine, – match, – map, inverse map, – compete (involves a max( ) operation) – attenuate, – scale – a nonlinearity (if not inherent)
![Page 32: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/32.jpg)
Constraints imposed by neural mechanics
• non-linearity
• limited accuracy and reliability
• limited amplitude range
• signal warp– pulse spread in dendrite means signal
interactions at distance from synapse of origin cannot depend directly on temporal fine structure seen in the axonal signal
![Page 33: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/33.jpg)
Neuronal circuit is constructed from cell pairs which implement reciprocal pathways with temporal or phase encoding
stage i Fi
stage i+1 Fi+1
Bi
Bi+1
inhibitorysynapse
excitatorysynapse
inhibitoryinter-cell
forward backward
V
t
V
t
DC 1.0 vs. DC 0.7
DC 1.0 vs. DC 0.5
![Page 34: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/34.jpg)
• Vectors are self “normalizing• Amplitude encoding range is not limited to cell
dynamic range• Capacitance (pulse spread) is friendly
– Increases temporal differentiation– Decreases effect of spatial location of synapse
• Only monotonicity required in combination to implement addition-like operation
• Devil-take-the-hindmost competition implemented by inhibitory signal derived from signal front –keeps meaningful signals in narrow range
Some advantages of phase encoding
![Page 35: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/35.jpg)
target 1
target 2
target 3
no targets
left
![Page 36: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/36.jpg)
![Page 37: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/37.jpg)
• Dendritic trees are non-homogeneous. i.e. local structure determines local signal interactions, global structure determines combination of local results
• All computation takes place in dendritic trees (in idealized cell).
• Signal interactions evolve primarily during rise time of dendritic pulse
• State can be held over between cycles to amplify signal differences
• Pulse length is long compared to propagation time: some location independence
![Page 38: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/38.jpg)
Intra-dendritic computation using phase in real neurons
From SR Williams, GJ Stuart, 2002, “Dependence of EPSP Efficacy on Synapse Location in Neocortical Pyramidal Neurons”, Science 295:1907-10
signal propagation
![Page 39: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/39.jpg)
sEPSPs
From SR Williams, GJ Stuart, 2002, “Dependence of EPSP Efficacy on Synapse Location in Neocortical Pyramidal Neurons”, Science 295:1907-10
![Page 40: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/40.jpg)
amplitude - rise time relation
From SR Williams, GJ Stuart, 2002, “Dependence of EPSP Efficacy on Synapse Location in Neocortical Pyramidal Neurons”, Science 295:1907-10
![Page 41: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/41.jpg)
phase difference – response amplitude function(also known as “coincidence detection”)
somaticsynapses
distal (620 um)synapses
distal (620 um)synapses
From SR Williams, GJ Stuart, 2002, “Dependence of EPSP Efficacy on Synapse Location in Neocortical Pyramidal Neurons”, Science 295:1907-10
![Page 42: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/42.jpg)
bbcol
stage b
stage m
stage r
input field
rm = r-match ri = r-intersect
rbkwd rfwd
bfwd bbkwd
mbkwd mfwd
mapping competition
1 2
3 4
6 5
7 8
9
10
rmcli
rm ri
11 subtract
1r
1r�
q1
g1
1b
1b�
maxb�
max q
max iqq
(1)
(2)
(3)
(4)
(5)
(6)
(9)
(10)
(11)
Signal equivalentsin algorithmic circuit
(7)
(8)
1m
1m�
![Page 43: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/43.jpg)
bbcol
stage r
input field
rbkwdrfwd
bfwd
bbkwd
mapping competition
1
2
6 5
9
10
rmcli
rm
ri
11 subtract
1r
1r�
q1
g1
1b
1b�
maxb�
max q
max iqq
(1)
(2)
(3)
(4)
(5)
(6)
(9)
(10)
(11)
Signal equivalentsin algorithmic circuit
3
4
![Page 44: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/44.jpg)
Signal relationships in neuronal circuit
0 5u 10u 15u 20u 25u 30u 0 600m 1.2 1.8 2.4 3
3.6
rm ri
bbcol
0 5u 10u 15u 20u 25u 30u 0 600m 1.2 1.8 2.4 3
3.6 bbcol
rm ri
recognition state
non-recognition state
bbcol inhibits late rm signalsthus blocking paired ri signal
![Page 45: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/45.jpg)
Is phase encoding the only way to satisfy the original requirements?
Encoding must support a sufficiently rich repertoire of computation– It must encode a sufficient range of values
with sufficient accuracy and discriminability– It must close under a sufficient set of
operations implementable with neural mechanics
Map-seeking circuits will work with any encoding that supports the operations listed earlier.
![Page 46: Attributes of a neural code for perceptual/cognitive computation Presented Feb 12, 2003 Mathematical Biosciences Institute Ohio State University David](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3a5503460f94c5719a/html5/thumbnails/46.jpg)
• Encodings must have started simple to have co-evolved with useful, robust mechanisms to implement operations on them.
An evolutionary caveat from engineering: complex and/or delicate systems generally do not work at first...but an evolutionary step has to work in “alpha release.”