KittyCat: a cognitive model of structure-form discovery

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FUNDAÇÃO GETULIO VARGAS

ESCOLA BRASILEIRA DE ADMINISTRAÇÃO PÚBLICA

E DE EMPRESAS

ANDRÉIA BRANDÃO DALTRO SODRÉ

KittyCat:

A Cognitive Model of Structural-Form Discovery

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Ficha catalográfica elaborada pela Biblioteca Mario Henrique Simonsen/FGV

Sodré, Andréia Brandão Daltro

KittyCat : a cognitive model of structural-form discovery / Andréia Brandão Daltro Sodré. – 2014.

50 f.

Dissertação (mestrado) - Escola Brasileira de Administração Pública e de Empresas, Centro de Formação Acadêmica e Pesquisa.

Orientador: Alexandre Linhares. Inclui bibliografia.

1. Cognição. 2. Desenvolvimento cognitivo. 3. Aprendizagem organizacional. 4. Probabilidades. 5. Tenenbaum, Joshua B. , 1972- . 6. Kemp. Charles. I. Linhares, Alexandre. II. Escola Brasileira de Administração Pública e de Empresas. Centro de Formação Acadêmica e Pesquisa. III. Título.

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ANDRÉIA BRANDÃO DALTRO SODRÉ

KITTYCAT: A COGNITIVE MODEL OF STRUCTURAL-FORM DISCOVERY

Dissertation delievered to Fundação

Getulio Vargas – FGV, as part of the requirements to obtain the title of Master in

Business Administration, advised by

Professor Ph.D. Alexandre Linhares.

RIO DE JANEIRO

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ABSTRACT

Cognition is a core subject to understand how humans think and behave. In that sense,

it is clear that Cognition is a great ally to Management, as the later deals with people and is

very interested in how they behave, think, and make decisions. However, even though

Cognition shows great promise as a field, there are still many topics to be explored and

learned in this fairly new area.

Kemp & Tenembaum (2008) tried to a model graph-structure problem in which,

given a dataset, the best underlying structure and form would emerge from said dataset by

using bayesian probabilistic inferences. This work is very interesting because it addresses a

key cognition problem: learning. According to the authors, analogous insights and

discoveries, understanding the relationships of elements and how they are organized, play a

very important part in cognitive development. That is, this are very basic phenomena that

allow learning. Human beings minds do not function as computer that uses bayesian

probabilistic inferences. People seem to think differently.

Thus, we present a cognitively inspired method, KittyCat, based on FARG computer

models (like Copycat and Numbo), to solve the proposed problem of discovery the

underlying structural-form of a dataset.

Key words: Cognition, Cognitive-model, Structural-Form Discovery, FARG, Kemp

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TABLE OF FIGURES

Figure 1: KT Step 1 ... 11

Figure 13: Copycat Step 1... 23

Figure 19: KittyCat Step 1 ... 31

Figure 25: Atlas ... 38

Figure 26 : (a) Spectrum extracted from justices' votes; (b) Hierarchy of the Bush cabinet. ... 47

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SUMMARY

ABSTRACT ... 2

TABLE OF FIGURES ... 3

SUMMARY ... 4

1 INTRODUCTION. THE IMPORTANCE OF COGNITION TO MANAGEMENT ... 6

2 KEMP & TENENBAUM’S MODEL ... 9

2.1 The imposition of structure ... 9

3 KT-STRUCTURES ... 11

4 FLUID CONCEPTS, FARG ARCHITECTURE AND THE COGNITIVE FLOW OF INFORMATION PROCESSING ... 16

4.1 Introduction to FARG architectures ... 16

4.2 Basic Components of the FARGitecture ... 17

4.3 High-level FARG Concepts ... 19

4.4 FARG Models ... 19

ANALTERNATIVE PROPOSAL TO KEMP & TENENBAUM’S MODEL... 28

5.1 Model Overview ... 28

5.2 System Architecture ... 28

5.3 Example ... 31

CRITICISM OF KEMP & TENENBAUM’S MODEL FROM A FARG PHILOSOPHY ... 36

7 CONCLUSION & FUTURE RESEARCH ... 41

7.1 Why is discovery of form important to Artificial Intelligence and computational cognitive science? ... 41

7.2 Why is this type of work important to management? ... 41

7.3 Future Research ... 42

REFERENCES ... 43

APPENDIX A ... 46

Hierarchical Bayesian model: forms, structures, and data ... 47

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1 INTRODUCTION. THE IMPORTANCE OF COGNITION TO

MANAGEMENT

Consider this summary of the case history of Polaroid’s transition from instant to

digital imaging given by Gavetti et al. (2005) in his paper. This case was result of extensive

fieldwork that the aforementioned author conducted at Polaroid and I take the liberty of

paraphrasing here for illustrative purposes.

Polaroid, founded in 1937, was a successful company in the photography industry

driven by instant-imaging products (camera and films) until the early 90’s. During its time,

Polaroid’s senior managers developed certain beliefs such as that all profits in this industry

were in the consumables — hence their untouchable “razor/blade” model — and that its

commercial success originated only from technological breakthroughs.

In the 1980’s, after noticing some weakness in the market, Polaraid ventured into

digital-imaging technologies and spent a substantial amount of money on R&D, even though

there was no market for these technologies yet. Digital-imaging managers started to question

the strategic implications of this new business model because it would shift the core to

hardware instead of consumables. At the same time, there were two other projects that

embraced the razor/blade model that had been successful so far. Because of these projects,

the conflict between senior managers who still believed in the razor/blade model and

managers of the new “hardware model” was not apparent.

In the early 1990’s, Polaroid had developed a working prototype of digital camera much superior to similar products by competitors, and digital-imaging managers believed

that this camera was essential for them to play a leading role in the consumer market.

However, senior managers opposed a camera with no printing device, as it wasn’t consistent

with the razor/blade model, which they were unwilling to abandon despite the continuous

evidence provided by the digital-imaging managers of how the emerging digital-imaging

landscape conflicted with their software-centered view. Thus, the digital camera release was

delayed and search efforts were pushed towards digital-imaging products agreeable with the

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Due to this failure and the inconsistency of digital-imaging with their traditional

business model, Polaroid turned away from digital imaging and when it started selling its

megapixel camera it was too late already and the camera had little success. By the end of the

decade, Polaroid had lost most of its early strength in the digital imaging.

After analysing the presented Polaroid case history, Gavetti arguments in his paper

that this case history displays the crucial role of cognition.

Polaroid’s early development of leading-edge technological capabilities in digital

imaging is hard to explain without considering the belief in technology’s primacy. For over

a decade, this belief led to massive investments in search efforts despite the lack of a tangible

payoff. Then, when a market for digital products emerged, senior managers discouraged

search activities that were inconsistent with their theory of how to be profitable in the

photography business, effectively destroying Polaroid’s core digital-imaging capabilities. The evidence suggests that cognition can be central to capability development by affecting

the efforts undertaken (Gavetti et al., 2005; Gavetti, 2005; Gavetti and Warglien, 2007).

Furthermore, in this case Gavetti brings attention to the contrast between top

managers’ cognitive inertia and digital-imaging managers’ rejection of a software-centered view for their emerging business, and how the fact that these top managers ignored cognition

at lower levels and decided which beliefs to guide the organization led it to rather negative

results. He highlighted the importance of studying the interplay between “cognitions”

differently situated in the hierarchy and in his paper he developed a model that shows that

managers’ cognitive representations of their strategic decision problem guide organizational search, and consequently the accumulation of capabilities. This is one of the many examples

that illustrates the importance of a deep understanding of cognition and how its application

to management can improve an organization’s chances of succeeding.

Cognitive science is as old as the times of Aristotle. However, cognition as we

currently know it is a relatively new field of study, which started to take its shape in the

1950’s with advances in the area of artificial intelligence (Simon, 1980). Its core interest is the understanding of the human mind. A very remarkable and interesting trait of cognitive

science is its interdisciplinarity, since it has important connections with anthropology,

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other disciplines. This characteristic makes it a very versatile science that can be of service

to many other areas — including management, in which we can find the underrated topic of

managerial cognition.

The beginning of managerial cognition is marked by the classic work of Schendel

and Hofer (1979), “Strategic Management: A New View of Business Policy and Planning”,

in which they describe a six step process to strategic management. Even though the cognitive

aspects are not explicitly mentioned, the process described by the authors is composed of

thinking activities that require cognition, therefore, managerial cognition was implicit in

their paradigm. According to Madhavaram et al. (2011), there seems to be an implicit

consensus among researchers that “managerial cognition is how and what managers think about and understand various firm issues that require action”. This definition limits

managerial cognition to the act of high-level thinking (e.g., strategy planning, analysis, etc).

However cognition is not limited to high-level thinking since numerous empirical studies

indicate that behavior is often cognitive and calculative (Simon, 1955; Porac et al., 1989).

Also, taking into account that behavior happens in all hierarchical levels and areas of

companies, it is not correct to limit managerial cognition to managers or the strategic level.

Thus, in a more proper and complete manner (more inclusive of all people in a

company), the definition of the academy of management, used by Forbes (1999, p.416) states

that managerial cognition is “how organization members model reality and how such models interact with behaviors”.

After this brief introduction of managerial cognition, one might still wonder what

might be the importance of this topic to the good study and pratice of management. Stubbart

provides a simple and fine explanation that syntheses exactly the relevance of managerial

cognition.

The chief appeal of cognitive sciences is that they promise to

fill the “missing link” between environment conditions and strategic

action. Environmental and organizational forces affect action

through executives’ thinking, and actions derived from thinking.

Organizational adaptation is an intelligent thinking process.

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Stubbart (1989) realized that managerial cognition is the aforementioned unnamed

missing link in Schendel and Hofer (1979) strategic management paradigm and proposed

that cognitive science principles could assist in managing complexities in strategic

management processes, in which managerial cognition plays a critical role.

2 KEMP & TENENBAUM’S MODEL

In their 2008 paper “The discovery of structural form”, Charles Kemp and Joshua B.

Tenenbaum proposed a very interesting computational model that learns different structures

and identifies the best form for a given dataset. It uses probabilistic inferences over a

pre-determined set of graphs, which were chosen due to their popularity, meaning they are useful

for describing the world and are more salient in the human mind when scientists seek formal

descriptions of a domain. In this study, graphs were chosen to represent structures and graph

grammars were used as a unifying language for expressing a wide range of structural forms

because the writers assume that the most natural forms are those that can be derived from

simple generative processes. In Kemp & Tenenbaum (2008), each structure can be formed

from “a single context-free production that replaces a parent node with two child nodes and

specifies how to connect the children to each other and to the neighbors of the parent node”.

2.1 The imposition of structure

Structures are imposed by most analytical methods. Clustering methods will always

find disjoint sets in data. Ranking (or order-based) methods project entities into a domain

that must be isomorphic to either N , Z , or R . Decision tree methods will create branchpoints

to classify the data, and so forth. Nature, on the other hand, is indifferent to our methods.

Nature presents us with a bewildering array of different forms and structures—as do

societies, firms, and other complex systems. Humans find structures by studying data and

carefully comparing and contrasting this information to previously experienced structures.

Linhares and Freitas (2010); Linhares and Chada (2013).Our analytical methods, however,

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 It may suggest hypotheses which are not warranted. A ranking of living

beings, scala naturae (or “the great chain of being”), was the unquestioned christian

doctrine until Carl Linnaeus proposed the tree alternative; this “great chain of being”

hypothesis—which goes upwards from rocks, plants, animals, man, spirit, angels and

god—suggested a hierarchy of beings that proceeds towards `greatness'; while the tree

of life hypothesis suggests a common ancestor, speciation, and the exploitation of niches.

 Moreover, the imposition of structures may blind us to important relations

hidden in the data. Prisoners generally self-organize into groups (gangs). Clustering is

able to capture the increased intra-group interaction that dimensionality-reducing

methods (such as χ 2 or the use of z -values) cannot. Ranking prisoners in order of 'violence propensity', or guards in terms of 'abuse of power propensity', will create the

previously mentioned rank anomalies and will most likely neither reflect nor predict

violence between individuals in any meaningful way. One needs to know how

individuals interact, not how they rank in a single dimension.

There is, however, no need to presuppose a form when analyzing data. Cognitive

scientists Charles Kemp and Joshua Tenenbaum have developed and algorithm enabling the

automatic discovery of form. While Kemp and Tenenbaum have published their work as a

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3 KT-STRUCTURES

In this section, a run of Kemp & Tenenbaum's model will be demonstrated. In this

specific round, the model is trying to discover the best tree structure available in a dataset of

american politicians. It is interesting to note that the model is forcing the dataset to fit in the

determined form of a tree and testing the better structure inside it. Furthermore, from the

start, all the components are part of the form already (they are not added one-by-one) and

start branching out from the same node of the tree.

Let's consider that the point from which all the elements are deriving as a point of

level zero and we shall call it root node.

Figure 1: KT Step 1

In the first step, we can observe that the model started constructing the tree structure

by separating the compenents “Bush” and “Cheney”, creating a new chunk from the

remaining dataset elements. Both become second-level nodes in relation to the root node,

whereas the rest of the elements are gathered together in a single first-level group. Thus the

tree structure is presenting two levels in total and the entire dataset is part of it already.

Figure 2: KT Step 2

Next, the structure adopted a triple-branch format, in which “Bush” was set aside on

a group of its own going back to the first level; “Cheney” was joined by “Rumsfeld”,

“Powell” and “Rice” on another second-level group; and the rest of the components were also grouped in another chunk in the second level. Apparently the system started realizing

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Figure 3: KT Step 3

The third step consisted of the model separating “Powell” and “Rice” into a new

second -level group containing only these two components.

Figure 4: KT Step 4

In the fourth step, the tree structure begins to develop a third level: “Libby” and “Rumsfeld”, components that previously belonged to the second level started a new third

-level group together, leaving the “Cheney” alone in their previous second-level group. The rest of the structure remained unaltered.

Figure 5: KT Step 5

After that, the model moved “Powell” to a second-level branch by itself and joined

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Figure 6: KT Step 6

Next, the model separated “Libby” and “Rumsfeld” into two different groups with a

single component in the third level that branched out from the same first level node.

Figure 7: KT Step 7

In the next step, the model moved “Rice” to be by itself at the second level, as it did

to “Powell” in step 5.

Figure 8: KT Step 8

In the following step, the model performed several actions: it swapped positions

between “Wollowitz” and “Rumsfeld”, letting the first be on a third level branch that derives from the same node at the first level that branches to “Cheney” at second level and “Libby” at third level; and the “Rumesfeld” moved to a second-level group that branches out from

the same node from which the group of “Myers”, “Armitage”, “Whitman” and “Feith”

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Figure 9: KT Step 9

After that, the model separated “Card” and “Ashcroft” and left them as two

components coming straight from the main node to the second level. In total, the structure

currently presents seven first-level nodes, nine second-level nodes and six third-level nodes.

Figure 10: KT Step 10

Next, the model disconects “Whitman” from its previous group keeping it at third

level like before, and branching out from the same node the group does.

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Finally, at step 12, the model performed several actions. “Armitage” and “Whitman” were part of the same cluster and were split apart. It moved “Armitage”, keeping it as a

third-level leaf node, and connected it to the first-level node from which “Powell” branches out.

“Whitman” was also maintained as a third-level leaf node and reallocated to branch out from

the same first-level node from which “Rice” does. Finally, “Wollowitz” got split from the

cluster it belonged with “Libby” and was placed alone as a second degree node, branching

out directly from the root node.

As a result, we have a tree-structure of the Bush cabinet. The structure logical and a

good representation of this group of American politics, however, it is not the best solution.

A hierarchy structure is the best solution to represent Bush's cabinet. We can notice

similarities of the optimal tree-structure to the hierarchical structure. For example, “Bush” is

alone on its branch and it is the only first-level leaf-node. The other leaf-nodes have lower

levels than him, showing he is the top level. When the tree-structure wants to represent

people under another person's power, it connects to the node from which the person with the

power branches out and it adds another level (e.g., “Armitage” is a third-level leaf node, connected to the first-leaf node from which branches out the second-leaf node “Powell”.

That means “Armitage” reports to “Powell”). The final structure has one first-level leaf-node, seven second-level leaf-nodes, five third-level leaf-nodes, comprising eight clusters

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4 FLUID CONCEPTS, FARG ARCHITECTURE AND THE COGNITIVE

FLOW OF INFORMATION PROCESSING

4.1 Introduction to FARG architectures

In Indiana University, located in Bloomington, there is a house called “Center for Research on Concepts and Cognition”, or CRCC, that works as the headquarters the group

of researchers, lead by Douglas Hofstadter, known as Fluid Analogies Research Group, or

FARG, as they refer to it. The name, though silly sounding (purposefully so), encompasses

the main beliefs and values that guide this group in its scientific endeavours. In the words of

Hofstadter, “the term fluid [...] exudes quite a clear image of flexibility, mutability, nonrigidity, adaptability, subtlety, pliancy, continuousness, smoothness, slipperiness,

suppleness”. For the FARGonauts (as the members refer to themselves) this ilustrates the properties of thoughts, which they believe emerge from several small, independent, invisible

and parallel subcognitive acts.

FARG focus on modeling mental processes on computer programs, however it is a

very hard attempt to explicit this group's central research ideas and goals. Nevertheless,

Hofstadter (1995) has presented a list of the most important themes that appear frequently:

 He talks about “the inseparability of perception and high-level cognition”, which basically states that the models generated by FARG attempts to model how human

perception works, and that they believe this perceptual architecture is the heart of

cognition. For instance, in the model Copycat (which will be explained more in depth

further on), the program perceives relationships between the letters and the strings, and

it makes analogies.

 There is the easiness of reconfiguring multi-level cognitive representations

and how those are connected by bonds of different types and strenghts, meaning that the

model is flexible and can turn some other new way to solve the proposed problem.

 Another recurrent theme is the idea of subcognitive pressures, which means

that when a concept is more “important” it will have more influence on the direction

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 These many pressures act commingling, in a nondeterministic parallel

architecture in which the several processes coexist peacefully.

 The simultaneous exploration of various potential possibilities according to

their degree of promise. So the program can look for several ways of answering the

proposed question and will keep on looking further on the options that seem more

appealing.

 One very important theme to this group is analogy making and variations on

a theme in high level cognition. Hofstadter believes that analogy is the core of cognition

so this theme is always central to this group's researches.

 The presence of deeper and shallower aspects of cognitive representations.

The degree of these aspects pose great influence on the contextual pressures imposed by

the system, the deeper aspects being more immune to said pressures, and the shallower

is more likely to yield to these pressures (to which we use the term “to slip”).

 The role played by the inner structure of concepts and conceptual

neighborhoods.

The present work does not attempt to explain in depth the aforementioned themes

because not all of them are used in the proposed work discussed on section five.

Nevertheless, it is important to mention all the recurrent themes providing the reader with a

more high-level understanding of what concerns FARG apart from the present approach.

4.2 Basic Components of the FARGitecture

Although each model generated by the Fluid Analogies Research Group is different

and unique in its own way, there are some components that frequently reoccur in the models.

These components seem very characteristic of the type of architecture used by the group.

Therefore, this section lists a few of these components that work as an identifying trademark

of FARG models.

Slipnet

The Slipnet is a structure that attempts to model the human mind's subtly

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memory that stores the concept types and its basic representation is that of a network of

interrelated concepts, in which concepts are nodes and conceptual relationships are links

with a numerical length (the “conceptual distance” between two nodes).Simply put, it works

as a storage for the knowledge that the system will use to solve its proposed problem.

One important feature of the Slipnet is that it is dynamic and responds according to

the situation it is presented with: it activates concepts and modifies conceptual distances

gradually according to the system's perceived relevance of the concepts. This phenomenon

encourages certain slippages to happen while the occurance of others becomes more remote.

Workspace

The Workspace is the area where structures are formed and the actions occur. It can

be visualized as a work site where there are various different randomly-distributed structures

which will be worked on simultaneously by the several small agents (codelets). The

structures are constructed and descontructred as necessary, in order to build up a coeherent

vision of the entire set of structures. The several different actions played in the Workspace

can go from scanning to describing, bonding, grouping, destroying and so on. The

Workspace can be compared to a working memory, which functions as temporary storage

and place for manipulation of information. (Baddeley, 1992; Baddeley & Hitch, 1974)

Coderack & Codelets

Codelets are small, simple agents that perform all the aformentioned acts in the

Workspace. Their actions as single units are very insignificant, so what is most important is

the emergent effect of their actions as a group . There are two types of codelets: bottom-up

codelets, which work on the Workspace in a random, unfocused manner; and top-down

codelets, which act in a more purposeful and specific manner, focusing on a particular goal.

When a codelet is created, it is stored on the Coderack — a codelet storage area where those

entities await for their turn to run — and is given a urgency-value, a number which determines its probability of being chosen from the selection of codelets in the Coderack.

The Coderack is replenished with codelets constantly and the selection of codelets inside of

it adjusts itself automatically according to the system's requirements, which influences the

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4.3 High-level FARG Concepts

Commingling Pressures

Pressures are implicit shifting forces, consequences of several interconnected events

in the whole system, that push certain types of processes to occur. Even though they are not

represented explicitly in the architecture, they are present in the system and perform a very

influential role. Basically, emergent pressures will determine the direction and action taken

by the system.

Parallel Terraced Scan

The parallel terraced scan is a simultaneous exploration of several different potential

pathways. Even though the system works with only one viewpoint at a time, there are several

parallel processes occuring that are unconscious and determined by the present pressures of

the system. These unconscious parallel processes play a big influence on the direction taken

by the system. For example, imagine a group of scout ants exploring a territory. There will

be a main line of ants going towards an objective and some random ants going around

different paths, reporting back, and changing the course of the main line to a more suitable

one with more potential direction.

Temperature

Temperature is a variable that monitors the stage of processing of the system and

controls the degree of randomness used in the decision-making. It assists overall system in

shiftingt from an initial bottom-up, open-minded mode to the top-down, closed-minded one.

Since the system does not have any information at the beginning, it does not matter which

codelets will run first, what to focus on and so on. However, the more the system explores

the situation, the more it becomes aware of the presented picture and it can start sending

more top-down, specific codelets that will strengthen the current viewpoint. The system

starts out with a high temperature and it decreases to lower temperatures the clearer its

viewpoint gets; thus, the value of the temperature demonstrates the present quality of the

system's understanding and its proximity to the best solution.

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In this section we discuss the FARG models which most inspired the proposed model

of this thesis, so the reader can better understand its origins and the similarities to the

previous models. These models are discussed in depth in the book Fluid Concepts and

Creative Analogies - Computer models of the fundamental mechanisms of thought by

Douglas Hofstadter and other FARG researchers.

Numbo

Numbo is a computer model based on the game “Le compte est bon”. Since By

simulating this game, Numbo displays the human mental behavior of fluidly grouping, taking

apart, and restructuting components in order to achieve a goal.

The game works as following: given five brick numbers (from 1 to 50) and three

possible arithmetical equations (addition, subtraction, and multiplication) how would you

arrange the brick numbers and arithmetical equations in order to achieve the target number

(from 1 to 150)?

An example of a puzzle by Numbo is to achieve the target 114 using the bricks 11,

20, 7, 1, 6. The answer is 20 x 6 - 7 + 1 or (20 - 1) x 6.

The name Numbo is inspired by another FARG model called Jumbo. Jumbo is a

computer model that solves the anagram puzzle Jumble. Since the present problem is very

similar to Jumble, but with numbers, the game was named Numble and the computer model

Numbo.

Numbo has three elements in its architecture: the Pnet, the Cytoplasm and the

codelets.

The Pnet is the network that has all the knowledge needed to solve the puzzle. It

activates concepts during the process of solving the puzzle. This concepts are nodes, which

are called Pnodes, and are stored inside the Pnet. Only very simple things are stored in the

Pnet, however, the activation of this simple things can help to find a solution to a complex

problem.

The cytoplasm is analogous to the workspace: it is the place where the building and

dismantling of structures happen. It begins with independent structures (called cyto-nodes)

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(e.g., brick, target, block), status (e.g., taken or free), and attractiveness (e.g., numerical value

that influences the nodes usage likelihood).

Finally there are the codelets, which are the small agents that work on the cyto-nodes

in the cytoplasm. The codelets are stored in the Coderack. They can perform many different

simple operations on the Pnet (e.g, activiting Pnodes), on the cytoplasm (e.g., comparing a

cyto-node to a target node) and on the Coderack (e.g., creating other codelets).

Copycat

Copycat is, according to the definition provided in the book Fluid Concepts and

Creative Analogies - Computer models of the fundamental mechanisms of thought , “a

computer program designed to be able to discover insightful analogies, and to do so in a

psychologically realistic way.” (Hofstadter & FARG, 1995, pp.205).

As the authors Hofstadter and Mitchell suggest, the domain in which Copycat

operates is very small but subtle. The main example of what Copycat does is illustrated by

the following puzzle: suppose the letter-string abc were changed to abd; how would you

change the letter-string iijjkk in “the same way”? In other words, given a letter-string that

was transformed into another one, you are supposed to transform a new letter-string

following (or copying, hence the name Copycat) the same intrinsic rules used by the previous

two letter-strings. Therefore it finds the answer of a letter-strings analogy puzzle.

Regarding its architecture, Copycat consists of four main components: a Slipnet, a

Workspace, a Coderack and temperature.

The Slipnet, as noted in the previous section, it is the source of knowlegde used by

the system to solve the proposed problem. It activates concepts and conceptual relationships

according to the way the program understands the situation at each codelet run, so it adjusts

itself dynamically, running until the system achieves the best result possible. An interesting

fact about the Slipnet is it adjusts itself after every codelet run; however when a new problem

is presented, the Slipnet returns to its original state and all of the adjustments are made from

scratch again. So, in this sense, Slipnet does not learn after solving a problem. Furthermore,

another important feature from Slipnet is that it allows concepts to slip from one to the other

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The Workspace is the site where structures are formed as the problem is worked on

by small agents, called codelets. At first, it is a bunch of unconnected raw data that, with

time, will start getting descriptions and being linked by perceptual structures, using the

information withheld in the Slipnet. The many tiny actions held in the Workspace such as

scanning, describing, bonding, destructing, grouping and so on will render the system a

coherent vision — viewpoint — and the increasing pressures will work in the direction sugested by said viewpoint. Even though there several objects in the Workspace and there

are several parallel processes and explorations occuring, it is simply not possible to give

attention to all of the elements present in the space; therefore, the system has to decide on

what objects to focus on, which is determined by the object's salience. The salience is a

function of the object's importance (the number of descriptions and degree of activated

concepts connect to it) and its unhappiness (few or no connections to other objects in the

Workspace).

The other important Copycat component is the Coderack, which stores the codelets.

The codelets are small agents that work upon the structures in the Workspace. A list of the

actions that a codelet may take on Copycat's Workspace is: scanning, describing, grouping,

bridge-building, destruction, bonding. One can also describe codelets as the proxies for the

pressures present in the system. This means that when the pressures are standard or

commomplace for all situations, bottom-up codelets are sent to the Workspace; whereas

when there are specific pressures, top-down codelets are summoned.

The temperature is the variable that demonstrates the present quality of the system's

understanding and its proximity to the best solution. The tendency is that the temperature

should start high and decrease as the structures are formed. However, the temperature does

decrease in a constant steady manner, and sometimes it even increases.

Next, we demonstrate how Copycat works to solve the aforementioned puzzle

displaying the steps it has executed until the best-fitting solution emerged.

Suppose the string abc were changed to abd; how would you change the

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Figure 13: Copycat Step 1

The first figure representing Copycat captures the moment when the program has run

110 codelets. The system does not have much structure at this point, hence the high

temperature. It has recognized each individual letter, created a brigde between the letters c

and d from the initial string and the target string, it has mapped leftmost letter a from the

initial string to the leftmost letter i at the string iijjkk, and it has noticed some bonds between

the neighbor letters. It has found bonds of sameness (as in j and j), successorship (as in a

and b or i and j) and predecessorship (as in b and c). It is interesting to note that, in the string

abc, the letter b is described as having competing bonds of both successorship and

predecessorship, which demonstrates some conflict of interpretation in the system; it will

have to deal with dissonant ideas competing against each other. Note that the system still

couldn't find a rule to make a transformation of the iijjkk letter-string. Also, the system has

created a chunk with the two j's, but still hasn't realized the sameness bond between the two

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The second figure displays the state of the program after a total of 260 codelets have

run. Some structure has emerged and an initial rule appeared (“replace letter category of rightmost letter by successor”). The temperature has dropped due to the emerging structure. Other chunks have been formed (ii and kk) and the abc string has adopted a successorship

bond only between the individual letters, in a staircase fashion, as the program notices it as

successor group. Also, now the system connects the rightmost c of the abc string to the

rightmost k of the iijjkk string.

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The following figure shows the state of the system after executing only 20 more

codelets. Now the rightmost c of the abc string is connected to the kk chunk. However, a

predecessorship bond has been found between the jj and the ii chunk, which is causing

conflict in the program. Due tp the destabilizing effect of the competing bonds in the system,

the temperature has risen, even though more codelets have been executed. This shows that

the temperature does not only drop, it rises when the system gets further away from a strong

solution.

The next figure shows the situation of the system after 415 codelets have run. A

successorship bond has been found between the ii and jj chunks and between the jj and kk

chunks, also, the system notices that the chunk jj is the in the middle of the iijjkk string. The

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In figure 5, after 530 codelets executed, the system finally realizes the that iijjkk is

a successor group and also it connects b, the middle component of the abc string, to the

chunk jj, the middle component of the iijjkk string. However, a is still connected only to the

letter i, and c went back to being connected only to the letter k (instead of to the chunks ii

and kk, respectively).

This last figure shows the final result of the program after 695 codelet executions.

Finally, the system has mapped a to the chunk ii, b to the chunk jj and c to the chunk kk.

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group by successor”, it applies this rule to iijjkk, producing the letter-string iijjll as the

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5 ANALTERNATIVE PROPOSAL TO KEMP & TENENBAUM’S MODEL

In this section, we will present an alternate proposal to Kemp & Tenenbaum's model

inspired by the FARG programs described in the previous section: KittyCat. The name

KittyCat is an hommage to the inspirations for this model: the work of Kemp & Tenembaum

(by discreetly using their names initials, KT, in the word Kitty) and the FARG models, which

have the tradition of using cat in their names (e.g.,Copycat, Metacat, Musicat). Furthermore,

the name seems fitting since a kitty-cat is a small type of feline, and this work still is in its

infancy compared to other FARG models that have already been implemented.

5.1 Model Overview

KittyCat is intented to solve the same puzzle proposed by Kemp & Tenenbaum (i.e.,

finding out the intrinsic best-fitting form and structure of a dataset) in a more fluid and

cognitivel-plausible fashion, simulating more precisely how the human mind would behave.

Kemp & Tenenbaum's model can work with three different kinds of input data —feature

data, similarity data, and relational data — and so will KittyCat. Even though the form of

the input can differ, the output will always consist of the same type of object: a graph

structure with a label indicating the category of the resulting structure.

The model should work with any of the three different kinds of input data. Each type

of data includes a set of entites (e.g., months of the year, animals, cities of the world, etc).

Each entity will start out being represented as single independent node, and during each run,

the nodes will be analysed, categorized, grouped and linked together in clusters until they

are organized in the structure and form that best suits them. For clarification, we we follow

Kemp & Tenembaum's usage of the word structure to mean the large-scale organization of

nodes (e.g., a ring, a hierarchy, a tree, etc) whilst the form is the particular organization of

the nodes within the structure (e.g., in the previous example of the Bush Cabinet, it is possible

to rearrange its form in a way that Bush is not the top of the hierarchy anymore).

5.2 System Architecture

KittyCat is comprised of the following major components: Atlas, Workspace,

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Workspace

It is interesting to begin describing the Workspace first because it contains the puzzle

to be solved. The Workspace may contain objects of the following types: nodes, links, groups

of nodes, labels, structures, and annotations. In its initial state, the Workspace contains the

independent individual entities of the presented dataset scattered around it. These entities are

nodes, for the expected output of this program is a graph structure constituted of said nodes.

It is important to realize that the Workspace only works with its present situation, so if

something has been discovered in a past codelet run, the new discovery should be identified

in the Workspace for the future runs, e.g. by using annotations or labeling of the nodes,

groups, structures, or any other element.

Consider a run where the input is a feature matrix and the model has discovered a

linear structure with three nodes in it. The model will label the structure (“linear”, “group 1”), groups (“group with 3 nodes in a linear structure”), links (“successorship”) and the nodes (“first”, “second”, “last”); and it will also put annotations on the links (“stronger”, “4 similar features”), on the group (“group with similarity on 4 common features”,), and on the nodes (“features 4, 8, 9, 10 seem interesting”, etc).

With these informations, the model will be able to continue modifying the Workspace

in more focused way, even though it will keep exploring other possibilities due to the parallel

terraced scan previously explained. The elements lables and annotations may change after a

new codelet run, new links may be formed, old links may be destructed, groups can be

dismantled or formed, structures may arise and disappear, and nodes may change

connections. All these actions will keep occuring in the Workspace until the best structure

and the best form emerge from the nodes.

Atlas

Atlas plays the role of the Slipnet in CopyCat, in the sense that it stores the concepts

that will be activated to solve the presented problem. The difference is that Atlas will activate

graph figures when the program discovers in the Workspace a structure similar to what it has

“seen before”. The idea is that activating certain types of graph structures would aid other

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If a match is found to some graph, then that could activate the slipnet for forms that are

appropriate for that graph (the one found in atlas). The finding of the structure can lead to

faster form emergence. Only the possible forms that match with the activated structure are

activated on the Atlas, whereas the ones that did not would remain innactive.

A few of the concepts or nodes we can find in the Atlas are graph structures (partition,

chain, ring, cylinder, tree, hierarchy, order, etc), “stronger”, “similar”, “weaker”, “parent

node”, “child node”, “group”, “first”, “last”, “second”, “third”.

As an example, consider that the program has to form a structure with the following

items: August, January, March, April, February, November, May, December, July,

September, June, and October. The model will analyze the situation and verify whether there

are graphs in Atlas that look similar to the proposed puzzle. Then, it might perceive a chain

structure, activating the chain concept in the Atlas. Later, it might trigger a codelet to verify

if the last item in the chain pattern is connected to the first item, thus leading to the discovery

of a ring structure. Note that the model does select a pre-determined structure to construct

(e.g., forcing the elements to form a ring). It recognizes in the Workspace patterns that are

recorded in the Atlas and it acts according to the activated concepts at each moment.

Coderack

The Coderack works the same way it does in the previous FARG models, as the

storage place where the codelets (small working agents) await for their turn to run. The

Coderack replenishes itself constantly with codelets and adjusts the codelet population

according to the new discoveries of the model. Like all other models, there are bottom-up

and top-down codelets, and codelets are randomly chosen from the Coderack based on

urgency level and Temperature. A few types of codelets that can be found on this model are:

 scanning codelet (low-level codelets that discover interesting characteristics,

relations and so on)

 labeling codelet (labels the elements in the Workspace)

 annotation codelet (adds annotations to the elements in the Workspace)

 linking codelet (creates links between the nodes)

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 {label, annotation, link, group} breaker codelet (destroys or erases previous

constructions)

 structure finding codelet (finds structures in the groups of nodes that match

with the Atlas content)

 stem codelet (creates any other codelet)

Thermometer

The Thermometer indicates the temperature of the Workspace. The temperature is a

variable that monitors the progress of the model. The Thermometer begins indicating a high

temperature, and then it decreases to lower temperature as the final optimal result of the

system becomes clearer. The most interesting aspect of the temperature is that, when it is

high, the system does not have a clarity on what is supposed to do, so it will act randomly

and make drastic operations (e.g., destroying a whole structure); however, when it is low,

the program acts in a more consistent manner. In that sense, the temperature plays great

influence on the urgency-levels bestowed upon the codelets in the Coderacks, thus

influencing the procedures of the model.

5.3 Example

In this section, we present how KittyCat would solve the same problem solved by

Kemp & Tenembaum in section three (3 KT-Structures).

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In the beginning, tthere is no structure apparent in the system's Workspace

whatsoever. All the components are scattered around randomly around the workspace as

single individual units. There are no bonds or connections mapped between the components.

The system still has no idea of what type of form should be used to organize the dataset of

these components, nor does it know the best structure within the best fitting form. So far, it

is all very unclear, and bottom-up forces should be used to try to find some kind of

relationship between the components. There is no hypothesis or theory to guide the process

at this stage. So the process is completely driven by the initial data, in a bottom-up fashion.

Figure 20: KittyCat Step 2

Finally, after some exploration, a relationship has emerged between the component

Libby and Bush, in which there is a connection from Libby, acting as a initial node, to Bush,

acting as an ending node. Since there are only two components and one connection, the form

so far could be perceived as a simple linear form. All the other components are still loose at

the workspace, awaiting more scannings to be designated to their proper arrangement. The

system is in a highly disorganized form and it is, at this point, not considering and

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Many additional rounds, and the system has come up with a ring form with a structure

that works from Libby, to Bush, and ending with Cheney that shall connect itself to Libby

to close the ring. In parallel, a bond has emerged from Rumsfeld to Myers, creating a simple

linear form with them. Very few components have been grouped up together yet. An analogy

to be made is that this stage is as if the system was building a puzzle and has grouped a few

pieces together, including pieces from different parts of the puzzle, but it still cannot figure

out what the final picture will be.

An initial form is activated: the system starts to consider the possibility that the

Cheney–Libby–Bush cycle may be the defining form underlying this data. However, this theory will quickly be discarded, as the system is unable to expand this cyclic form, or to

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In the next scenario, the system has realized that the ring form was incorrect and has

dismantled it into a linear form, structured in a fashion that it starts with Bush, that connects

with Cheney and this latter connects itself to Libby. In addition, a new connection has been

mapped connecting Powell to Armitage. It is interesting to note that in this instance, the

system has unmade the first connnection it had found in its earlier steps (Libby to Bush

connection) as well as the ring connection. This is a clear demonstration that the system is

flexible and fluid, in a sense that it can “change its mind” about some past action or try to

find other solutions that might seem more appealing at a given time.

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This next step is of pivotal importance, for a hint of a draft of a complete picture

starts to emerge. Analysing the picture, it is possible to say that the conclusion should arise

soon, even though it is not completely clear the final form it will take. Almost all of the

components now have connections, except for two, and they are assembled in 5 chunks,

which should be connected somehow to create the final form with its best-fitting structure.

Rumsfeld now is connected to Feith and to Myers. The system presents a big chunck

originating from Bush, that connects to Wolfowitz, Rice, Ashcroft, and finally Cheney, this

latter connecting to Libby. This big form seems like a hierarchy, as does the form generated

by the trio Rumsfeld, Feith and Myers.

At last, in a sudden flash, the system finally realized the form and the structure the

dataset should adopt that would best suit it. All the loose chunks were connected to Bush,

becoming part of the previously biggest, and now only, chunk of the dataset. The components

adopted a form of hierarchy, the form that the system had identified in a few steps before

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6 CRITICISM OF KEMP & TENENBAUM’S MODEL FROM A FARG

PHILOSOPHY

After the brief review of FARG and a brief description of a FARG-like system given

above, one should ask: how does the FARG system differs from Kemp and Tenenbaum's?

Moreover, and more importantly, why should a FARG system be proposed as an

alternative?

Let us enumerate some crucial issues:

 K&T's system employs Breadth-first Search

Kemp and Tenenbaum's system works by first selecting a previously fixed form and

working on it until it has modelled the entire dataset into that form. The system employs a

single, unique `graph grammar' at a time. Only after fully processing a particular form may

it move to try the next possible form, and a comparison of results is brought out in the end,

finally selecting the form with the `best-fit'.

This approach does not seem flexible and fluid, as the human mind is. For starters, it

follows a rigid sequence between the forms. Moreover, it is completely unable to `change its

mind' and reconfigure the model into another form–regardless of the dataset; regardless of how the form seems to be unable to account for the data. This is something that humans do

quite capably (Hofstadter and FARG, 1995; Linhares, 2000; Linhares and Brum, 2007;

Hawkings and Blakeslee, 2004).

 Works from the whole to the individual unit

Kemp and Tenembaum's system starts with an overwhelming cluster containing all

entities, FARG systems start at the other extreme: entities have no connection to each other.

FARG systems employ linking (perceived) related entities, not on splitting clusters. In fact,

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Consider now, for instance, how humans play games, such as Sudoku, or Chess, etc.

It seems that one wants to find relations between pieces, or between Sudoku's quasi-empty

permutations. It seems that the mind is under a process of joining entities.

It certainly does not seem as if one has a bad (i.e., low-quality) global view of the

entire space, as implied by Kemp and Tenembaum's starting point and subsequent cluster

splits. Consider, for example, Kemp and Tenembaum's example of geography, in which the

latitudes and longitudes (of cities) are given as input. Let us think in terms of countries.

Imagine we have a map of the world's nations bearing no names on it, and we should fill in

the names. Kemp and Tenembaum's system would begin by placing random names in all

nations (i.e., a low-quality, all encompassing cluster). It would then proceed to divide this

all-encompassing view into more reasonable clusters, gradually finding that the USA and

Canada are close. A person, on the other hand, may be unaware of where Moldova is, but

may still join countries that have been strongly associated, such as USA–Canada, Brazil–

Argentina, Germany–France, or China–Japan. It seems that it is more psychologically

plausible to start from isolated elements and slowly bring them together than to start with a

random, all-entities-included stochastically, viewpoint.

 Atlas graphs

Here is one characteristic which is lacking in both Kemp & Tenembaum's model and

FARG, though it is FARG-like, and may bring a contribution to future models. Imagine a

slipnet for a form-finding system. As seen above, items on the slipnet may bring top-down

pressures (i.e., hypothesis, or expectation-driven pressures) to reconfigure one's view. Such

a slipnet would certainly contain all possible forms available to the system, such that if the

bottom-up discovery process activates a (set of) particular form(s), there should be increased

`attention', or energy expended exploring those possibilities first. At this point we go over

technical details that may be of interest in devising a computational model: Atlas graphs are

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Figure 25: Atlas

Atlas of graphs: This is the entire family of graphs with up to 6 nodes. Given that

each of these graphs are associated with some forms, but not with most, they may enable a

faster, and more fluid, activation of top-down forms.

In Figure 13 we see an `Atlas graph' with all possible graphs with up to 6 nodes. In a

FARG system, by finding some initial relations, one of these graphs will be active—and the

triggering of its corresponding graph in the Atlas is very fast. Because each graph in the

Atlas will be associated with some, but not all, top-down slipnet `form' nodes, the activation

of a graph in Atlas may activate suitable slipnet nodes, bringing pressures towards a

particular form. These pressures may, if strong enough, eventually force the system to

reconfigure the entire system state, in order to align the data with the expectation brought

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Consider the example of the purple graph at the lowest rightmost position: this graph

is associated with circular forms. Therefore, if the system creates a graph like this one, the

circular form should be activated, and the system may attempt to reconfigure all the nodes

(those within and outside the 6-node graph) in a circular manner.

This would be a more fluid approach to the design of the system. Kemp and

Tenenbaum's model remains fixed in a single form throughout a run, inspite of any evidence

that there may be a particular underlying form worthy of consideration. This is exactly akin

to what Hofstadter describes below: entering a bookstore and reading the first book

cover-to-cover, instead of browsing the possibilities and exploring only those that seem attractive.

This point, is, of course, related to the idea of a temperature-managed system.

 Temperature (frustration, entropy, etc) & parallel terraced scan

The flow of information processing in FARG systems is given by Temperature.

Temperature enables what Hofstadter has termed `parallel terraced scan':

On entering a bookstore, do you read the first book you come across from cover to

cover, then the next one, and so on? Of course not. There is a profound need for protecting

oneself from this sort of absurdity. People develop ways of quickly eliminating books of

little interest to them and homing in on the good possibilities. This is the idea of the terraced

scan: a parallel investigation of many possibilities to different levels of depth, quickly

throwing out bad ones and homing in rapidly and accurately on good ones. (The term is

mine, but much of the idea was present in an implicit form in Hearsay II.)

The terraced scan moves by stages: first one performs very quick superficial tests,

proceeding further only if those tests are passed. Each new stage involves more elaborate

and computationally more expensive tests, which, if passed, can lead to a further stage - and

so on. Furthermore, "passing a test" is not an all-or-nothing affair; each test produces a score,

indicating how promising this line of investigation appears at that stage. One uses this score

to determine the urgency of follow-up codelets (if indeed the score is high enough to warrant

any). This provides the desired layeredness to the evaluation of the quality of a potential

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If a system has true (hardware) parallelism, it can perform quick tests on many items

in parallel, slower tests on a smaller number of items in parallel, and so on. On the other

hand, if the hardware is serial, the various tests making up the parallel explorations must

instead be interleaved, so that many possibilities can be simultaneously probed, with some

being in the earliest stages of testing, and others at various stages further along in the

scanning process. Hofstadter and FARG (1995), p. 107.

If one wants an `optimal' form-discovery system, it may make sense to apply the flow

of information-processing of Kemp and Tenembaum's model, given by a strict breadth-first

search. However, does that seem psychologically plausible? Aren't we faced with confusion,

cognitive dissonance, hesitation, as we face an unknown problem? Do not things seem to get

easier as we struggle to represent the problem? It seems that Hofstadter's model captures

something crucial about both System 1 thinking and System 2 thinking: the ability to quickly

accept (or discard) information (System 1 thinking), and the ability to engage in attention, or

energy-intensive problems. We note here that in Hofstadter's philosophy, the very idea of

System 1 versus System 2 seems too binary, too clean-cut, too detached from each other, as

his models provide a smooth and fluid interplay between both systems. Instead of a chasm

between System 1 and System 2, one has a whole continuum between these two forms of

thought. A clear example of this apears in the Numbo project: people quickly ``see'' that

20x20=400 , but not the results of 17x23 . Yet, people seem to know that the result is `close'

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7 CONCLUSION & FUTURE RESEARCH

7.1 Why is discovery of form important to Artificial Intelligence and

computational cognitive science?

Consider a robot, a chess-playing program, a data mining system, and so on.

At one point, the system must be pre-programmed to deal with numbers; and more

specifically what kinds of numbers: a 32-bit integer is completely different from a 64-bit

float. And both numbers are different from a string such as `Hello world'. And all of those

are different from a branching point, given by a tree, which is still different from a loop. The

process of discovery of form enables the system to discover, on its own, given only the

dataset, that numbers belong to orders, trees belong to hierarchies, loops belong to cycles,

and so forth. By providing the first analysis of the discovery of form problem we believe that

Kemp and Tenenbaum's work brings us a monumental contribution.

Numerous things that should previsouly be explicitly pre-programmed can now be

discovered, and, if devised under a FARG philosophy, re-configured on the fly. What

initially looks like a vector, or a sequence, of integers can adapt a float, such as 3.1415. All

it takes is for the system to have discovered that numbers are formed by an order, and the

system will be able to correctly place (or process) the float between the integers previously

seen.

Numbo, for instance, has trees, chunks, and numbers. All of these can be discovered,

instead of pre-set by a programmer. Much like the human minds discovers a large number

of relationships and dynamics.

7.2 Why is this type of work important to management?

As we have mentioned in the introduction, cognition plays a great strategy role on

management and companies benefit immensely when they properly use managerial

cognition. Cognitive Science is a very new study field and its application to management are

even more recent. KittyCat is a cognitive model that simulates how to discover structure and

form within a dataset in a cognitively-plausible manner. This model allows us to understand

how the human mind works. Therefore, this model contributes to increase our knowledge on

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However, even though these subjects are new, they show great promise as interesting

areas that will increase our knowledge of many fields related to management, for example,

behavior and decision-making. A practical consequence of this work is its contributions to

managers improving their management strategies as well as their decision-making.

Cognitive science principles could assist in managing complexities in strategic

management processes.

7.3 Future Research

In summary, we have studied the discovery of form problem from a FARG

philosophy. The suggestions for future improvements are listed below:

 We limited ourselves to describing in detail how KittyCat works with the

most interesting type of input data — a matrix of feature data. Further exploration of how

the model works with the other two types of input data featured on Kemp &

Tenembaum's work would be interesting.

 Future research should find ways to allow KittyCat to work with a greater

number of types of input data or, ideally, any type of data .

 To better simulate how a human mind works, KittyCat should understand

more about the world and be able to work with an input entities that are specified using

natural language text (e.g., “tray”, “lamp post”, “man”, “tripod”, “dog”). The objective

is to make the model work without a predetermined set of features and derive new

features from fuzzy concepts. For instance, if we give KittyCat the previous list of

example words of natural language, the model should find the structure and form among

them. A fuzzy concept that has to come up to achieve the result is the number of legs (or

supports) each object has (e.g., a tray has zero legs, a lamp post has one, a man has two

legs, a tripod has three legs, a dog has four legs). Thus, a good structure is an order that

begins with the tray and ends with the dog, according to the number of legs.

 This paper describes theoretically how KittyCat works, thus leaving the

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