ACT Theory Research Paper

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ACT is a theory of human cognition that posits particular ways of representing knowledge and the mechanisms by which such knowledge is acquired and used (Anderson 1983, 1993, Anderson and Lebiere 1998). The theory is implemented as a computer simulation system that generates the theory’s predictions, thereby facilitating quantitative comparisons with experimental data.

1. What’s In A Name?

The etymology of the acronym ACT is the subject of some debate. The original definition, Adaptive Control of Thought, has not been consistently used, and several books written about the theory suggest alternative candidates, e.g., The Adaptive Character of Thought (Anderson 1990) and The Atomic Components of Thought (Anderson and Lebiere 1998). However, these publications postdate ACT’s modest beginnings by more than a decade, making the simpler moniker A Cognitive Theory seem the most parsimonious answer.

2. Architectures And Models

Among computational systems designed to model cognition, there is a critical distinction between a cognitive architecture and a cognitive model built within an architecture. A cognitive architecture defines a specific way of representing knowledge and a fixed set of mechanisms for processing knowledge. A cognitive model, on the other hand, specifies the knowledge that is required to perform a particular task. Any one architecture supports a wide variety of models, all of which use the same mechanisms to capture behavior in different tasks, just as the brain presumably employs a common set of mechanisms across a variety of tasks.

The ACT theory is a cognitive architecture. It provides mechanisms for the retrieval and learning of facts (declarative knowledge) and the selection, application, and learning of skills (procedural knowledge). All cognitive models built within ACT share these mechanisms; what differs across ACT models is the task-specific knowledge (i.e., the facts and skills themselves) input to the system. ACT models have successfully fit behavioral data across a wide variety of tasks, including arithmetic, navigation, categorization, and game playing (see Table 1). The success of these ACT models across such varied domains provides support not only for the models themselves but for the explanatory power of the ACT architecture.

 

This research paper focuses on the current version of the ACT theory, called ACT-R (Anderson and Lebiere 1998). Nevertheless, a historical sketch of the theory’s evolution and how it relates to contemporary research are presented as well as a brief discussion of future research issues.

3. Basic Features Of The Theory

The four main tenets of the ACT theory are as follows:

(a) the ability to perform a complex task can be decomposed into separate pieces of knowledge;

(b) these pieces of knowledge are learned through experience, i.e., using a piece of knowledge is akin to practice;

(c) at any given time, the current focus of attention (also called the goal) influences what knowledge is used; and

(d) there are two types of knowledge, declarative (for facts) and procedural (for skills), that have distinct representations and learning mechanisms.

Declarative knowledge is represented as nodes in an associative network. The more activated a given node, the more easily the corresponding fact can be accessed. Each node has an associated base-level activation B that increases each time the fact corresponding to that node is accessed (learning) and decays with time (forgetting) according to the equation

where t is the current time, t_j is the time of the jth use of the node, and d is a global decay rate. The quantity B offers a summary description of a node’s past history of use and hence a reasonable estimate of its likelihood to be needed in the future.

Each link between two nodes in the network has a continuous-valued quantity S that measures the strength of association between those two nodes. The current focus of attention works by selecting a subset of nodes in the network to be attended. Each attended node gets a share of a limited amount of attentional activation W. (Because attentional activation is limited, the more nodes in the focus, the less attentional activation for each.) This activation then propagates from each attended node to related nodes in the network in proportion to the corresponding link strengths. This attentional activation produces context effects because only those nodes related to the current focus of attention receive extra activation.

The total activation at node i is the sum of its base-level activation B_i and the attentional activation it receives from nodes in the focus of attention:

where the sum is over attended nodes j. Retrieval of facts is determined by the total activation of the corresponding nodes. Specifically, the node that is retrieved is the one whose total activation plus some added noise is highest, given that this sum is above a global threshold. This added noise represents stochasticity in the system. The time it takes to recall this node decreases exponentially as a function of its (noisy) activation which, combined with Eqn. (1), produces a power-law speedup with practice.

Procedural knowledge is represented by a set of condition–action pairs called production rules (e.g., IF the goal is to add two numbers a and b, and the fact that c is the sum of a and b can be recalled, THEN say c is the answer). Each production has several associated quantities that reflect how useful it has been in past applications. These quantities are learned by experience and used to compute an estimate of the expected gain from applying each rule. For example, the cost associated with a particular production rule is the weighted average of the rule’s past costs of application (measured in units of time) and a prior estimate of cost. When several rules are candidates at the same time, the one whose expected gain plus some added noise is highest gets selected. In this way, production rules that have been more useful (i.e., more successful and less costly) in the past are more likely to be selected. In addition, each piece of procedural knowledge is strengthened with each application, and that strength decays with time. A production rule’s speed of application increases exponentially with strength.

The ACT theory also posits more complicated mechanisms by which production rules and declarative nodes are initially created. In both cases, the goal plays an important role in the form that new knowledge takes. These separate mechanisms highlight ACT’s distinction between acquiring new pieces of knowledge and refining the continuous quantities associated with each piece of knowledge. Moreover, these two modes of knowledge representation—symbolic (nodes, production rules) and sub-symbolic (activations, costs, strengths)—make ACT a hybrid system. This distinguishes it from wholly symbolic (e.g., Soar) and wholly sub-symbolic (e.g., connectionist) systems.

4. Historical Development

ACT has been under development since the 1970s. It began as a theory of semantic memory and now encompasses learning, memory, problem solving, attention, perception, and action. The following pro-vides a brief sketch of its development and places each version of the theory in its historical context. Until the 1970s, mathematical models were the typical formalism used to describe and predict cognitive psycho-logical phenomena. A disadvantage of mathematical models, however, is that they are limited in the complexity of processes they can describe. Thus, to provide a mechanistic account of complex cognitive processes, computational models began to be developed. The first well-defined version of the ACT theory, called ACTE (Anderson 1976), was one such model. It introduced the distinction between declarative (i.e., factual) and procedural (i.e., skill-based) memory and the notion of declarative activation.

By the 1980s, however, some researchers were questioning whether the development of computational models (and the theories they implemented) was sufficiently constrained to produce reasonable models of the ‘true’ underlying representations and processes (e.g., Anderson 1978, Newell 1973). One approach that reduces this problem involves developing models within a cognitive architecture, where a fixed set of representations and mechansims are used to test a variety of models. That is, models are constrained to work within the strictures of the architecture. The next version of the ACT theory, ACT* (Anderson 1983) was a cognitive architecture, like others developed around this time (Newell 1990). ACT* extended its predecessor by specifying an activation calculus for declarative knowledge and a new mechanism for acquiring procedural knowledge.

Besides using ACT* to model a variety of task domains—from language processing to paired-associate learning—this version of the theory was applied to the practical problem of improving computer-aided instruction. So-called ‘intelligent’ tutoring systems were built based on ACT* cognitive models of algebra problem solving, geometry theorem proving, and computer programming (e.g., Anderson et al. 1989, 1990). Because these models could solve the required problems in each domain, they enabled the corresponding tutoring systems to follow students’ problem-solving, give feedback when students made a mistake, and offer hints when students were confused. Moreover, because these systems tracked the steps students were taking and hence the knowledge they were using, specific predictions of the theory could be generated and tested in this scaled-up, real-world learning context.

The latest incarnation of the ACT theory, ACT-R (Anderson 1993, Anderson and Lebiere 1998), was developed in the 1990s, inspired by a rational analysis of cognition (Anderson 1990). Among other things, ACT-R includes a refined activation calculus and a more plausible mechanism for acquiring procedural knowledge. These changes were designed to reflect the way human cognition adapts to the structure of the environment. In addition, ACT-R has been put to the toughest challenges in testing its fidelity to empirical data: ACT-R models have been able to fit fine-grained, multivariate data simultaneously across several experiments (e.g., Anderson and Matessa 1997), and they have captured patterns of performance in individual subjects across tasks (e.g., Lovett et al. 2000). In sum, the ACT theory has evolved into its current form by virtue of the guiding force of several kinds of constraints. Throughout ACT’s development, experimental data have been used to test the veridicality of the theory. In some cases, this empirical constraint has invoked a reevaluation of some aspect of the theory (e.g., single-trial learning of production rules). More generally, even when the theory’s predictions have been met, refinements were made so that more detailed, fine-grained datasets could be modeled. Besides these empirical constraints on the theory there are theoretical constraints imposed top-down from the architectural status of ACT’s claims. That is, an ACT model may need to be designed in a certain way so that the knowledge it specifies is sufficient to perform the given task when ACT mechanisms are applied. Finally, based on the rational analysis of cognition (Anderson 1990), constraints have been imposed on the theory so that it includes the kind of processing that is necessary and sufficient to meet the demands of the environment.

5. Future Issues

The ACT theory is still under active development. An extension has been added (called ACT-R PM, Byrne and Anderson 1998) that incorporates perception and motor modules (e.g., eyes, ears, and hands). This extension enables the system to model interaction with the environment. In addition, ACT models have been developed for a variety of new domains, including complex, dynamic tasks such as air-traffic control. In some cases, the data sets being modeled even include eye-movement protocols. Yet another area of development involves exploring the relationship between the algorithmic level of description of the ACT-R computer simulation system (cf. Marr 1982) and a corresponding neural level implementation.

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