Modelling Innovation – some options from probabilistic to radical

Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 1
Modelling Innovation
– some options from probabilistic to radical
Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

The problem
Whilst there are many simulations/models of
the spread or uptake of innovations…
...the process of innovation itself is
generally not modelled

Talk Outline
1.  Kinds of innovation (derived from Boden, M. (2004)
The creative mind: myths and mechanisms, Routledge)
2.  Three examples of modelling exploratory
innovation
3.  Some thoughts about how to approach modelling
transformative innovation

Innovation 0: Probibilistic
•  When an unlikely event occurs (from a known
distribution)
Examples:
–  two people who went to school together happen to
meet in a departure lounge 20 years later
–  A spore of fungus happens to infect a petri dish with a
bacterial culture on it
•  Not really innovation in a meaningful sense
•  But it may trigger an innovation (of another kind)
•  However, this is how innovation is represented in
many simulations!

Innovation 1: Combinatorial
•  When there are a number of possible
‘components’ and you find the combination of
them (that does something)
Examples:
–  The right cut, size, colour and material for a t-shirt
–  Choosing the options for a new kind of family car that is
both attractive yet cheap enough to sell well
•  This is hard when there are a large number of
possibilities and when the number of acceptable
solutions is low
•  One can systematically compare solutions and
maybe find an optimal combination

Innovation 2: Exploratory
•  Where the process of discovery is path-dependent
and the paths branch in complicated ways
Examples:
–  Finding the right genome (for some purpose) using a
sequence of mutations and sexual recombinations
–  Discovering how to synthesize a chemical
•  This is closer to pure research – one might not
know the outcome before one gets there
•  Not possible to optimize, this is more a case of
discovering something new (or a new process)
•  Might be useful in a new way, or be a new kind

Innovation 3: Transformational
•  When something changes the way we think about
things – changes the landscape of discovery
•  Examples:
–  When Newton connected the movement of everyday
objects and the planets via his laws of motion
–  A new understanding of a relationship with someone
when you discover something about their past
•  Adds a new ‘dimension’ into the search for
solutions, or changes the paths for exploration
•  Something humans are quite good at, but this can
be misleading – just because you can think of
something in a new way does not make it so

Personal vs. Historical Innovation
Just because something is new for an individual does
not mean it counts as an innovation for society
For it to count as a historical innovation:
1.  It has not to be commonly known or adopted already
2.  It is recognized as a particular kind of thing
3.  And judged as an innovation by the ‘field’ of people
that judges that kind of thing
(Kahl, CH. (2012). Creativity is more than a trait – It's a
relation, Doctoral thesis, University of Hamburg).
It may be that something is not immediately recognised
as an innovation but may be so later due to the impact
of the innovation or the field changes etc.

Two Examples of Modelling
Exploratory Innovation
1.  A model of mathematical discovery and scientific
publishing
2.  A model of making things
In both:
•  Knowledge is structured in complex ways
•  How to “get to” the desirable structures is difficult to
predict before you do, but there are clues in the
intermediate stages (i.e. the search space is hard but
not random)
•  Items have a dual use: as ends in themselves, but
also as tools to help make new items or make items
more efficiently
•  There are naturally “gateway” discoveries that the
means to obtaining many other targets

Mathematical Discovery and Scientific
Publishing
Example 1

The test-bed problem
•  The theories are those of classical propositional
logic with connectives: ¬, ∧, ∨, →, ↔, T, F
•  formulated as a “Hilbert System” with:
–  14 axioms
–  1 rule, Modus Ponens (MP) (explained shortly)
•  110 designated “target theories” taken from
textbooks
•  New theories developed by taking applying MP to
to existing theories
•  Makes for a fairly tough problem - space of
theorems is more than exponential in size

Agent-1
Agent-2
Structure of the Simulation
The Journal
The Axioms
MP
MP

Action of the MP inference rule
yyxx →→→ ))((
)()(( aaaa →→→
BA → (Major Premise)
A (Minor Premise)
)( aa →
B (Inference)

Agents
•  Agents have two (limited) stores, for knowledge
(minor) and techniques (major)
•  Each iteration each agent:
1.  Decides what new items of knowledge to add to its
private stores from the published set, also which to
drop (both major and minor).
2.  Decides which major premise and what set of minor
premises it will try with the MP rule and add any
results to its (minor) store.
3.  Decides which of its private knowledge (that is not
already public) it will submit to the journal
•  Agents may “panic” if they have not discovered
anything within a certain number of iterations
and replace their knowledge (minor or major)

The Journal (the Journal of Artificial
Sentences and Successful Syllogisms)
•  The journal is the public repository of knowledge
(accessible to all)
•  Each iteration the journal:
1.  Makes a short-list of submissions that meet basic
criteria (e.g. novelty, number of vars.)
2.  Ranks the short-list using a weighted score (in this
case, shortening, shortness, past success of
submitter, number of variables)
3.  Chooses from the ranked short-list (e.g. top N,
randomly, probabilistically etc.)

The Experiment
•  20 agents over 50 iterations
•  Each agent stores 4 major and 27 minor premises
as its current knowledge and submit all
unpublished formulas they find
•  1 journal, selecting for (in descending order)
shortening; shortness; prestige; num vars.
•  Vary the number of formula the journal publishes
each iteration from 1…10
•  Results are averages over 25 independent runs
for each setting

Example output from a run
…
Iteration 3
agent 3 found '->' ('->' A ('->' B C)) ('->' B ('->' A C))
agent 3 found '->' ('->' A ('->' ('->' B C) D)) ('->' ('->' B C) ('->' A D))
agent 6 found '->' ('->' A ('->' B B)) ('->' A ('->' A ('->' B B)))
agent 6 found '->' ('->' A ('->' A B)) ('->' A B)
agent 6 found '->' ('->' A B) ('->' ('->' B A) ('->' A B))
agent 17 found '->' ('->' A ('->' A B)) ('->' A B)
agent 19 found '->' ('->' A B) ('->' ('->' C A) ('->' C B))
agent 19 found '->' ('->' A B) ('->' ('->' C ('->' ('->' A B) D)) ('->' C D))
Iteration 4
agent 7 found '->' ('->' A B) ('->' ('->' ('->' A B) C) C)
agent 7 found '->' A ('->' ('->' A B) B)
agent 13 found '->' ('->' A ('¬' A)) ('¬' A)
agent 15 found '->' ('->' A ('¬' A)) ('¬' A)
Iteration 5
Iteration 6
…

Number of formulas in public domain
0
100
200
300
400
500
600
0 10 20 30 40 50iteration
totalnumberformulafound
njp=1
njp=2
njp=3
njp=4
njp=5
njp=6
njp=7
njp=8
njp=9
njp=10

Number of targets found
10
10.5
11
11.5
12
0 10 20 30 40 50iteration
totalnumbertargetsfound
njp=10
njp=9
njp=8
njp=7
njp=6
njp=5
njp=4
njp=3
njp=2
njp=1

Total number found by agents (also num.
submitted for publication)
0
20
40
60
80
100
120
140
160
180
0 10 20 30 40 50iteration
totalnumberformulasubmitted
njp=1
njp=2
njp=3
njp=4
njp=5
njp=6
njp=7
njp=8
njp=9
njp=10

(Average) spread (the SD) of numbers of
formulas found by agents
0
1
2
3
4
0 10 20 30 40 50iteration
sdofnumbersagentsfound
njp=1
njp=2
njp=3
njp=4
njp=5
njp=6
njp=7
njp=8
njp=9
njp=10

Number found by agents
(a single run, njp=2)
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50
Iteration
Numberfoundbyagents

Number found by agents
(a single run, njp=10)
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50
Iteration
Numberfoundbyagents

Some issues that could be
investigated in this test-bed include:
•  Is any norm on methods for discovering new
knowledge is counterproductive? (Feyerabend)
•  What is the effect of the framework (within which
knowledge is expressed) on the structure of new
knowledge? (Kuhn)
•  When and how do social processes act to
increase the reliability of knowledge collectively
produced (or otherwise)? (Merton, Popper)
•  Is it helpful to have an inviolate core of
knowledge/techniques that is not open to
revision? (Lakatos)

A Model of Making
Example 2

The String MakerWorld
•  Things in this model are strings, e.g. ‘ACC&BA’
•  They are made form a finite number of ‘elements’ {A,
B, C…} and the two special symbols: {&, >}
•  Only certain strings can be extracted from the
environment (randomly determined at the start). All
other strings have to be made from these.
•  Only certain target strings can have inherent value
(randomly determined at the start). These can be
‘used’ to get that value
•  Strings can be joined/split by hand at & but to get any
other kind of longer string you have to use a tool
(another string with “>” in it that can change strings)

Simple Example
Say an agent was in the following situation:
Available in environment: A; A>; AA; AB; B>; BA; BB;
A&A; A&B; AAA; AB>BA
Has use value to agent: AB; A&B; AAA; AAB; ABA; B&A;
BBA; BBB; A&AA
Possible sequences of actions by agent:
•  Get A&B then immediately use it
•  Get A and BA then join these to make A&BA
•  Get A&B, split this into A and B, then join these to
make B&A and use this
•  Get AB use tool AB>BA on it to make BA, use it

Rationale behind String MakerWorld
•  Simplest world that allows the complexity of
making to be explicitly represented
•  Working out how to make valuable strings is hard,
which gives value to good plans (and hence
motivation for trading/sharing plans)
•  Control over which resources each agent has
access to can add heterogeneity in production
•  Control over the target strings each agent can
directly use can add heterogeneity of need
•  Heterogeneity of resources and needs gives
motivation for the trade/sharing of objects

The Model
•  Agents are patches but can interact with others in any
pattern they choose/learn
•  Things are explicitly tracked with their own properties
(which matter structurally)
Agents are
implemented
as patches
Object and its string
owned by an agent
Some objects are
complex, this one soft-
joined from smaller
parts
Some objects are simple, this
one composed of a single
“element”
This object is a tool, in
this case adding a soft
join into the string
(allowing it to be maybe
separated later)
The arrow indicates a sale/
transfer of an object from one
agent to another

Plans
•  Plans (the sequence of actions needed to make
particular things) are separate from the things
•  Agents sometimes do things experimentally (ATM
at random) to see what they can make
•  Agents remember how they made things in terms
of plans – the actions necessary to get any
particular outcome
•  Agents remember the better value plans and
preferentially execute those again
•  These plans could be sent/shared/licensed
between agents

Some example plans learnt by an
agent
value 3.25: realise [BAA split-right [B&BAA get]]
value 1.5: sell [B get] (patch 0 0)
value 1.25: realise [BAA split-right [B&BAA split-right
[B&B&BAA join [B split-left [B&BAA get]] [B&BAA get]]]]
value 1.25: sell [B split-left [B&BAA get]] (patch 2 0)
value -1: join-random
value -1.5: B split-left [B&BAA get]
value -2: get-random
•  Note that alternative plans to make the same things
might be remembered, but with different costs
•  Plans can be arbitrarily complex, thought each action
has a small cost associated with it, so more complex
plans will tend to have lower values (unless they
result in a more valuable result)
•  Agents prefer to re-use plans with higher value

The (current) main simulation loop
Continually (each tick), agent:
Considers a number of plans (including the
default random ones) with a bias towards more
valuable ones:
Until one works:
Assess next plan to see if it would work
If so, do plan!
If new, compile and remember plan
If have too many plans in memory, maybe forget
one (with a bias towards the less valuable ones)

Number of things made in 10 different runs
0
20
40
60
80
100
120
140
160
0
23
46
69
92
115
138
161
184
207
230
253
276
299
322
345
368
391
414
437
460
483
1
2
3
4
5
6
7
8
9

Number of different things made in the 10
runs
0
5
10
15
20
25
30
0
22
44
66
88
110
132
154
176
198
220
242
264
286
308
330
352
374
396
418
440
462
484
1
2
3
4
5
6
7
8
9

Average number of tools found in 10 runs
0
1
2
3
4
5
6
0
21
42
63
84
105
126
147
168
189
210
231
252
273
294
315
336
357
378
399
420
441
462
483
1
2
3
4
5
6
7
8
9

Average String length in the 10 runs
0
5
10
15
20
25
30 0
21
42
63
84
105
126
147
168
189
210
231
252
273
294
315
336
357
378
399
420
441
462
483
1
2
3
4
5
6
7
8
9

Average Number of things for sale in 10
runs
0
5
10
15
20
25
0
17
34
51
68
85
102
119
136
153
170
187
204
221
238
255
272
289
306
323
340
357
374
391
408
425
442
459
476
493
1
2
3
4
5
6
7
8
9
10

Average Maximum Plan Value in the 10
runs
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0
16
32
48
64
80
96
112
128
144
160
176
192
208
224
240
256
272
288
304
320
336
352
368
384
400
416
432
448
464
480
496

Average Wealth in the 10 runs
0
200
400
600
800
1000
1200
1400 0
18
36
54
72
90
108
126
144
162
180
198
216
234
252
270
288
306
324
342
360
378
396
414
432
450
468
486
1
2
3
4
5
6
7
8
9
10

Standard Deviation of Wealth in the 10 runs
0
100
200
300
400
500
600
700
800
0
16
32
48
64
80
96
112
128
144
160
176
192
208
224
240
256
272
288
304
320
336
352
368
384
400
416
432
448
464
480
496
1
2
3
4
5
6
7
8
9
10

Issues we might explore…
…include:
•  Changing the heterogeneity of needs, from everybody
has similar needs, to all different
•  Explore the conditions under which more centralised
manufacturing or markets emerge
•  Explore the impact of introducing new technology
(something equivalent to 3D printers)
•  Looking at how the structure of communication (for
plans or selling/sharing items) effects things
•  Maybe even wilder topics, e.g.
–  what if all objects contain their own plans
–  or come with tools to disassemble/reassemble/fix it
–  How might the norms of agents impact on the outcomes

Towards Modelling Transformative
Innovation
•  In order to represent transformational modelling
one needs to be able to change the way agents
view what they are doing
•  This means they have to
a)  HAVE a view of what they are doing
b)  use this to make representations of their world
c)  then use these for discovery (e.g. exploratory
discovery)
d)  sometimes be able to change their view
•  In other words a Model of Modelling itself

A language of
representation
model1
model2
model3
Goals to evaluate
success of
models
Actions
Perceptions
Some of what Model of Modelling would
involve
A world sufficiently
complex to make
this complex
machinery
worthwhile
A language of
representation
model1
model2
model3
Goals to evaluate
success of
models
Actions
Perceptions

Conclusions
•  Modelling more sophisticated kinds of innovation
is possible within agent-based simulation
•  At the moment these models are quite abstract,
but there is no reason why these kinds of
approaches should not be applied to modelling
innovation within firms and universities
•  A better understanding of the creativity that occurs
could help us know how to encourage and/or
direct it
•  Simpler models of innovation are almost certainly
insufficient to do this

The End!
Bruce Edmonds:
http://bruce.edmonds.name
Centre for Policy Modelling: http://cfpm.org
The slides will be available at:
http://slideshare.net/BruceEdmonds

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