Modeling of Cognitive Agents

Dariusz Plewczynski

ICM, Interdisciplinary Centre for Mathematical and Computational Modelling

University of Warsaw, Pawinskiego 5a Street, 02-106 Warsaw, Poland

Abstract. Agent-based Modeling (ABM), a novel computational modeling pa-

radigm, is the modeling of phenomena as dynamical systems of interacting

agents. Here, we apply this methodology for designing cognitive agents that are

allowed to perform categorization process of input training items. The internal

agent structure, as in presented previously brainstorming algorithm, and it is

equipped with the set of basic machine learning, or clustering algorithms,

which allow it for constructing prototypes of categories. Agent links prototypi-

cal categories with the subsets of training objects (so called prototypes for a

category) during the simulation time. The equilibration process is described

here using the mean-field theory, and fully connected cellular automata net-

work of different categories. The individual outcomes of clustering, or machine

learning algorithms are combined in order to determine the most effective parti-

tioning of a given training data into the set of distinct categories. The dynamics

of cellular automata network simulates the higher level of information integra-

tion acquired from repetitive learning trials. The final categorization of training

objects is therefore consistent with equilibrium state of the complex system of

linked and interacting machine learning methods, each representing different

category. The proposed cognitive agent is the first autonomous cognitive sys-

tem that is able to build the classification system for given perceptual informa-

tion using ensemble of machine learning algorithms.

1 Introduction

The one of main challenges in cognitive sciences is the symbol-grounding problem. It

is originating in long term discussions how to build the cognitive representation of the

environment (so called world) using some internal states of intelligent individual. The

relation between a symbol, a real-world object, and a concept applicable to the object

is typically implemented using semiotic triad, which links a subset of objects, the

concept for a category, and a symbol that represents this category. The underlying

mapping between the concept and the object is performed using a method, i.e. a pro-

cedure to decide whether the concept applies to an object or not. The idea of semiotic

triad was first introduced by Peirce (1839-1914) as a method for linking things and

symbols used to describe them. Further work by Searle [1] supported idea that semio-

tics is not only theory of language, but also a theory of production of meaning. The

main driving force behind the development of semiotics is a practical purpose. We

use things or events as signs that facilitate the navigation in complexity of life.

Plewczynski D..

Modeling of Cognitive Agents.

DOI: 10.5220/0003307200280036

In Proceedings of the 1st International Workshop on AI Methods for Interdisciplinary Research in Language and Biology (BILC-2011), pages 28-36

ISBN: 978-989-8425-42-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

We apply similar approach to study the categorization process within Agent-

Based Modeling (ABM). The ABM method extends the cellular automata-like models

[2], to more complex computational setups, for example by introducing the asyn-

chronous interactions between agents. Agent is defined here as a subsystem distin-

guished from its environment by some functional characteristics. Moreover, it has

some ability to perform an autonomic action, i.e. dynamical interaction with sur-

rounding world without external control. The presently used agent models are ranging

from simple ones (simulations of a disease spreadout, predator-prey systems), to

complex ones (insects colonies, immune responses modeling, financial markets etc.).

Typically ABM simulations require an explicit representation of the space, on which

agents are located. The most important step in the definition of an ABM is to intro-

duce a set of rules in order to describe the changes of system’s state.

Here, we use specific type of an agent, namely cognitive agents (CA) that are

equipped with brainstorming algorithm, i.e. several clustering, or machine learning

algorithms, which are running in parallel. The complex internal structure allows to

perform classification tasks on training objects, and storing learned knowledge in

terms of predictive models that can be further applied to unknown cases. This mimics

the ability of natural cognitive systems (for example neuronal system, living cell, or

human brain) to deal with incoming information. We need such advanced logic build

into the agent model in order to construct the symbolic representation of external

world objects in terms of symbols that represent grounded categories of training data.

Agent models the grounding process by training its internal learning method to

map a subset of observed objects into single category. The “name” of this category

(i.e. the sign denoting it in internal language of an agent) is a symbol representing it.

The learned predictive model is the proposed concept that describes the category, and

it is applicable to objects in order to assign them with a proper symbol. The semiotic

triad first proposed by Peirce is therefore modeled on the level of single agent within

Agent Based Modelling paradigm. The set of semiotic triads representing several

categories (or symbols) builds up the semiotic network. In the case of simple cogni-

tive tasks, i.e. when either a set of objects is not large, or a number of categories dis-

tinguishing those objects is small.

Summarizing, cognitive agents can be used as a model complex system for study-

ing the details of categorization process, the emergent phenomena, patterns learning,

selection of rules, or in general knowledge discovery. We provide here the founda-

tions of proposed cognitive ABM framework, and initial computational results. The

simulations are performed for given training information randomly selected from

available training data, agent during the course of simulation is building its semiotic

network of input training data, linking proposed categories with selection of training

objects. The results are compared with categorization studies performed within last

decade, especially in the field of psycholinguistics. Perspective applications of this

approach are also sketched. They could include modeling of perceptual grounding of

symbols using text mining techniques, context information, and visual or auditory

sensor data categorization in robotics.

2 Design of Cognitive Agent

Our model of categorization process is based on agent based modeling (ABM) para-

digm known from many applications in informatics [3], life [4-11]and social sciences

[12]. Our present model extends previous results, where probabilistic cellular automa-

ta (CA) model of opinion formation in groups of individuals was simulated by Le-

wenstein et al. [13] using social impact theory introduced by Latane [14, 15]. The

intermittent behavior was observed with a variety of stationary states with a well-

localized and dynamically stable clusters (domains) of individuals, who share minori-

ty opinions [13]. In the social impact theory a group of N agents influence of a given

agent opinion, where the level of influence depends on three factors. First, the social

strengths of all members of the whole group; secondly, their social distance from the

selected individual; and finally their total number N. Kohring [16, 17] extended La-

tane's theory to include learning. Plewczynski [18, 19] solved analytically the model

in the continuous limit and the Cartesian space with learning rules. Hołyst et al. per-

formed numerical simulations in simplified geometries, also provided the mean-field

approximation of the social impact theory [20-23].

Here, I present an application of agent based modeling in simulating the process

of categories formation. Each agent (so called “cognitive agent”) is equipped with a

machine learning, or clustering algorithm. The mathematical method allow them to

classify training examples based on their features, find differences between them and

categorize them into separate, or overlapping categories. Moreover, the “cognitive

interaction” between two agents is proposed by introducing guessing games, which

allow for coupling of categories not only by sharing the same training data, but also

by exchanging proposed models outcomes. The topology of a network of interactions

between agents is defining their “cognitive space” (for example the Cartesian space,

fully connected, nearest neighbors coupling, or hierarchical geometries). The final

stable semiotic landscape is defined here as the stationary state for such population of

agents.

The agent based model of category formation is based on several assumptions:

2.1 Discrete Categories

We assume that training data can be described in the form of several distinct or over-

lapping categories. In the first case, the crisp clustering can be applied and training

examples can be divided into separate groups of objects using their features. In the

second case, the full separation cannot be performed, and fuzzy clustering techniques

have to be applied in order to assign objects to the proposed categories. Both cluster-

ing techniques are optimized using some internal parameters, or validity indices. In

some cases, the multiobjective optimization can be used, which simultaneously opti-

mizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clus-

tering solutions. In the case of machine learning algorithms we deal with binary class

prediction (only two categories are described), or a set of distinct categories, each

described by different machine learning model. Here, internal parameters of ML

algorithms may seriously impact the performance of each method, therefore the di-

versity between agents is achieved. Our population of agents consists from N cogni-

tive agents. When a given training or testing object is presented to each agent, its

internal state is described holds one of several distinct categories (from 1 up to k,

where k is the number of categories constructed by an agent). These states are binary

1, ..,

= , similarly to Ising model of ferromagnet. In most cases the machine learn-

ing algorithms that can model those agents, such as support vector machines, decision

trees, trend vectors, artificial neural networks, random forest, predict two classes for

incoming data, based on previous experience in the form of trained models. The pre-

diction of an agent answers single question: is a query data contained in class A

(“YES”), or it is different from items gathered in this class (“NO”).

2.2 Disorder and Random Strength Parameter

Each learner is characterized by two random parameters: persuasiveness

and sup-

portiveness

that describe how individual agent interact with others. Persuasiveness

describes how effectively the individual state of agent is propagated to neighboring

agents, whereas supportiveness represent self-supportiveness of single agent. In

present work I assume that influential agents has high self-esteem, what is supported

by the fact that highly effective learners should have high impact on others in meta-

learning procedure. For example, we can select

()

p f precision i=

and

()

frecalli=

in the case where agents are modeled as single machine learning procedures. In gen-

eral the individual differences between agents are described as random variables with

a probability density

()

, with mean values

∑

and

∑

. Similarly

to the social influence theory, the quality of predictor in some way affect its influence

strength, when the final optimization of meta-learning consensus is done.

In the case of meta-learning procedure the persuasiveness

represents here the

ability of learning agent j to persuade agents who hold the opposite state to switch to

having the same state as j. The supportiveness

represents the ability of learning

agent j to support agents who hold the same state, so not only the self-support of an

individual agent (to itself), but the support that an agent gives to other agents who

share the same state as it has.

We use here cognitive agents that are allowed to perform categorization process

of training objects, therefore trying to autonomously build the classification system

for given perceptual information. Each agent during the simulation time is building its

semiotic network of input data, linking proposed categories with subsets of objects

(so called prototypes for a category).

2.3 Learning Space and Learning Metric

Each agent is characterized by a location in the learning space, therefore one can

calculate the abstract learning distance

(

)

,dij of two learners i and j. The strength of

coupling between two agents tend to decrease with the learning distance between

them. Determination of the learning metric is a separate problem, and the particular

form of the metric and the learning distance function should be empirically deter-

mined, and in principle can be a very peculiar geometry. In present manuscript, I

select the fully connected learning space, where all distances between agents are

equal

()

,1dij

. This particular geometry is useful for example in the case of simple

consensus between different yet not organized machine learning algorithms, where no

group of learners perform significantly better than others.

The interaction between agents dynamically shape their semiotic networks, adjust

the categories in order to match them between different individuals, and finally lead

to equilibrium, stable shared semiotic landscape of training data. The equilibration

process is described here using the mean-field theory, and fully connected cellular

automata network of agents.

2.4 Learning Coupling

Agents exchange their opinions by biasing others toward their own classification

outcome. This influence can be described by the total learning impact

that ith

agent is experiencing from all other learners. Within the cellular automata approach

this impact is the difference between positive coupling of those agents that hold iden-

tical classification outcome, relative to negative influence of those who share opposite

state, and can be formalized as

() ()

II I

iij ij

σσ σσ

=−−+

∑∑

⎛⎞⎛⎞

⎜⎟⎜⎟

⎝⎠⎝⎠

(1)

where

(

)

and

()

are the functions of persuasiveness and supportiveness

impact of the other agents on the

i-th agent. It should be noted here that the persua-

siveness

represents here the ability of agent j to persuade agents who hold the

opposite state to switch to having the same state as

j. On the contrary the supportive-

ness

represents the ability of agent j to support agents who hold the same state,

i.e. preventing them from switching to the opposite state. That is, persuasiveness

represents the propensity of

j to cause other agents to switch to her state, and suppor-

tiveness represents her propensity to keep them there.

The social interaction between agents are modeled as guessing games between a

pair of agents, where the first agent presents to the second one a samples randomly

selected from different classes of its prototype categorization.

2.5 Meta-learning

The equation of dynamics of the learning model defines the state

of ith individual

at the next time step as follows:

(

)

(

)

ign I

iii

σσ

=−

(2)

with rescaled learning influence:

()

iij ij

Ns p Ns p

σσ σσ

=−−+

∑∑

(3)

I assume a synchronous dynamics, i.e. states of all agents are updated in parallel. In

comparison to standard Monte Carlo methods the synchronous dynamics takes shorter

time to equilibrate than serial methods, yet it can be trapped into periodic asymptotic

states with oscillations between neighboring agents.

The dynamics of cellular automata network simulates the higher level of informa-

tion integration acquired from repetitive learning trials, so called the dynamics of

semiotic landscape for the whole population. The final categorization of training

objects is therefore consistent with equilibrium state of the complex system of inte-

racting agents. The individual outcomes of clustering, or machine learning algorithms

are combined in order to determine the most effective partitioning of a given training

data into the set of overlapping categories.

2.6 Noise

The randomness of state change (phenomenological modeling of various random

elements in the learning system, and training data) is given by introducing noise into

dynamics:

(

)

(

)

ign I h

iiii

σσ

=− +

(4)

where

is the site-dependent white noise, or one can select a uniform white noise,

where for all agents

= . In the first case h

are random variables independent for

different agents and time instants, whereas in the second case

h are independent for

different time instants. I assume here, that the probability distribution of

is both

site and time independent, i.e. it has uniform statistical properties. The uniform white

noise simulates the global bias affecting all agents, whereas site-dependent white

noise describes local effects, such as prediction quality of individual learner etc.

Each category consists of several prototypes; therefore it is grounded in classified

data objects. The population of autonomous agents establishes via communication a

repertoire of perceptually grounded categories that is shared among them.

3 Concluding Remarks

Intelligent agents theory is a fascinating topic in modern science [24-28]. Decision

making transitions depend to high degree on global factors influencing an ensemble

of independent learners. On the other hand, those changes are dependent to a high

degree on individual decisions (predictions) that are based on agents’ attititudes.

During consensus, i.e. the final decision making, the reciprocal influence is critical as

each learner exchange its opinion with others. In my approach, I assume that external

factors acting on each learner are present during only the first phase of meta-learning,

where initial states for a population of learners are setting up. Yet, both processes

even if acting on different time scales, are important for understanding the computa-

tional intelligence process.

In this manuscript I have presented the statistical theory of meta-learning. In my

approach I select long-range coupling between agents, as opposite for example to the

Euclidean two dimensional learning space, where only nearest-neighbors are coupled.

This assumption is well supported by the fact that we are typically focused on only

equilibrium, stationary states. The fully connected learning space lets agents evolve

faster in comparison to other types of cellular automata. In addition, all agents influ-

ence each other, therefore we avoid local minima traps for the global system.

Each learner is characterized by two random parameters: persuasiveness

and

supportiveness

that describe how individual agent interact with others. The random

strength parameters simulate different individual features of learning agents. In prin-

ciple one can define both parameters in various different ways. In the case of a set of

machine learning algorithms, each of them can be described by its intrinsic parame-

ters affecting precision of single classification model of training data. In general case,

several different types of machine learning algorithms can be used as individual

learners. There, the distribution of quality of local prediction can be described as

random providing that algorithms differ significantly between each other in terms

both of the quality of prediction (classification accuracy), recall values (the ability to

memorize the positive items in the training dataset), or precision (the ability to pre-

cisely predict the classification of training items).

The other definition of those parameters (persuasiveness and supportiveness) can

enhance the method persuasiveness (the value of

), if the method has the state

=+ , and make its p

value lower when the opposite state is taken. In this way, it

allows to speed up the consensus process by forcing system to reach equilibrium state

more rapidly, yet pushing it to the +1 decision based on the selected training dataset.

This can cause several problems with overtraining, therefore some limitations of this

approach should be taken into account. The actual solutions presented in this paper,

yet do not depend strongly on the selected form of those parameters. Anyway we

assume that they are some random variables describing the variety of individual deci-

sions in the ensemble of learners.

There two time scales in the system. The first time scale is related to the fast evo-

lution of individual learners. When input testing data is presented to the system, each

learner respond by its own single prediction. This local prediction of each agent is

done very rapidly, almost instantly. Then those individual predictions are processed

by cellular automata algorithm in order to find the stationary state of the system. This

part is denoted as integration of information. As it was shown above, such stationary

state has the form of minority clusters surrounded by the sea of majority prediction.

Therefore, the final consensus prediction given by the majority rule, still preserves

non-orthodox solutions, allowing for fast adaptivity of the system when training data

pattern is changed. The time scale for this integrative process is relatively long in

comparison to individual predictions, therefore very fast (preferably optimized for

parallel processing) cellular automata software implementations have to be prepared

in order to apply described above formalism in real life problems. In the statistical

model presented here, I assume that there is no coupling between those two time

scales. Therefore I neglect all details of individual evolution of learners, focusing our

attention for integration phase of incoming local information into single, consensus

answer.

The population of cognitive agents performs classification tasks on training ob-

jects, in order to build the shared complex system of signs and meanings. for given

perceptual information. Charles Peirce introduced semiotics as a theory of human

experience mediated by our ability to reflect upon it and create explainations (repre-

sentations). According to Peirce, the major research endeavour of semiotics is to find

out what are the conditions for meaning to occur in human experience. Thus semiotcs

directly addresses the issue of meaning: "What is wanted, is a method of ascertaining

the real meaning of any concept, doctrine, proposition, word, or other sign. The ob-

ject of a sign is one thing; its meaning is another. Its object is the thing or occasion,

however indefinite, to which it is applied. Its meaning is the idea which it attaches to

that object, whether by way of mere supposition, or as a command, or as an assertion"

(Peirce, C. 1931-58 Collected Papers of Charles Peirce in Eight Volumes. Eds: A.

Burke, C. Hartshorne and P. Weiss. Cambridge: Harvard University Press, 5.5).

Acknowledgements

This work was supported by Polish Ministry of Education and Science (N301

159735) and other financial sources. I would like to thank dr. Joanna Rączaszek –

Leonardi (Psychology Department, University of Warsaw), Prof. M. Lewenstein

(ICREA & ICFO, Barcelona, Spain) and Prof. M. Niezgodka (ICM, University of

Warsaw, Warsaw, Poland) for stimulating discussions.

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