The computational dimensional overlap model was first published in detail in Kornblum, Stevens, Whipple and Requin (1999) and explored in its most generalized and complete form in Stevens (2000). The model is a localist connectionist network model (Grainger & Jacobs, 1998; Quinlan, 1991; Rumelhart, McClelland, et al., 1986) that implements most of the major assumptions of the original dimensional overlap representational model, as well as adding some new assumptions that allow the model to make precise quantitative predictions and account for the time-courses of consistency effects.
Like all connectionist models, the computational dimensional overlap model consists of a network of interconnected processing units, where each unit is very simple, characterized by a single variable (called the unit’s “activation”) that changes over time as a function of input to the unit and determines the output of the unit to be transferred to other connected units. Each unit represents a discrete stimulus or response feature, such as the stimulus color, the stimulus location, or the response word. In connectionist models of performance, activation in a stimulus feature unit increases when that feature is present in the environment, and the feature is identified as present in the environment when the activation reaches a critical identification threshold. Correspondingly, activation in a response feature unit increases as evidence for the correct response increases, and when the activation reaches a critical response threshold that response has been selected.
The overall structure of the original dimensional overlap process model is preserved: the units in the network are organized into two layers: the stimulus processing units are in the first layer (functionally equivalent to the “stimulus encoding” stage of the process model) and a response processing units are in a second layer (functionally equivalent to the “response production and execution” stage of the process model). Activation of the units in the stimulus layer is not allowed to trigger activation in the response layer until the activation reaches the stimulus identification threshold: this allows the network model to implement the basic assumption of stage-like processing from the original model.
Like the original representational model, the computational model also provides two pathways for activation to pass from the stimulus to the response: a set of controlled connections that associate each stimulus unit to the unit for the response that it is assigned to by the mapping instructions (this corresponds to the “response identification” path in the original representational model); and a set of automatic connections, if there is dimensional overlap between the stimulus and the response, that associate each stimulus unit to the corresponding unit in the response as determined by the dimensional overlap between the sets (this corresponds to the “automatic response identity and verification” path in the original process model).
Finally, the computational model preserves the fundamental assumption of the dimensional overlap model about the locus of consistency effects. Specifically, S-S overlap is modeled using automatic connections between units within the stimulus layer that represent different (but corresponding) stimulus features, while S-R overlap is modeled using automatic connections between stimulus units and response units that represent corresponding stimulus and response features.
Although the architecture of the model depends on the task being represented, the model of a Stroop task (Type 8) illustrates all three types of overlap: irrelevant S-R, relevant S-R and S-S. This is represented in the network using three distinct sets of automatic lines: automatic lines between pairs of corresponding stimulus units, automatic lines between relevant stimulus units and response units, and automatic lines between irrelevant stimulus units and response units. In the illustration here, the network is modeling a congruent mapping: the automatic lines from the relevant stimulus units to the response units run parallel to the controlled lines from the relevant stimulus units to the response units.
(Note: in addition to the corresponding automatic lines, there are also inhibitory non-corresponding automatic lines between units that represent features that do not align. These connections have a negative weight, so that activation in a stimulus unit will decrease the activation in a non-corresponding response unit when they are connected by automatic connections. These inhibitory connections are not shown in the diagram simply for the sake of simplicity.)
To understand exactly how the model works, consider what happens in these units when a stimulus is presented.
When the stimulus is presented, activation begins to accumulate in units of the stimulus layer that correspond to features of the stimulus. At that point all the response units are clamped to zero, and are immune to any and all attempts at activation.
When there is S-S overlap, activation will be accumulating in two of the stimulus units: one corresponding to the relevant stimulus feature and one corresponding to the irrelevant stimulus feature. If the stimulus is S-S consistent, then the activation in the irrelevant stimulus unit will be connected with a positive automatic line to the relevant stimulus unit, enhancing its overall input and making its activation grow faster. On the other hand, if the stimulus is S-S inconsistent, then the activation in the irrelevant stimulus unit will be connected with a negative automatic line to the relevant stimulus unit, inhibiting its overall input and making its activation grow more slowly. As a result, the stimulus identification process is slower when the stimulus is S-S inconsistent than when it is S-S consistent.
When the level of activation in a relevant stimulus unit reaches the stimulus threshold, the stimulus has been identified. This triggers a control process that unclamps the response units and initiates the accumulation of activation in the response layer. When there is irrelevant S-R overlap, activation of the irrelevant stimulus unit may also begin feeding its output to the response units at this time.
The model postulates that the inputs to both the relevant and the irrelevant stimulus units start at the same value – say 1. The input to the relevant unit stays at that level, whereas the input to the irrelevant stimulus unit decays shortly after its onset. Moreover, there is increasing evidence that it may decrease below zero for longer processing times, leading to negative activation of the irrelevant stimulus and the reverse-Simon effect in the Hedge and Marsh task (see Kornblum & Stevens, 1997, November).
As the input to the irrelevant unit start to decay, the activation level of that unit levels off and starts to decrease as well, and ends up in an inverted U shape. In the meantime, the activation level of the relevant unit increases until it reaches threshold.
When there is irrelevant S-R consistency in a task, the response units are being given input from both the relevant stimulus unit (via the controlled connections) and the irrelevant stimulus units (via the automatic connections). When the irrelevant stimulus is S-R consistent, activation of the irrelevant stimulus unit would lead to the automatic activation of the corresponding response unit which is also being activated by the controlled line. This additional activation would interact with the accumulated activation in that response unit, thus being facilitative. On the other hand, when the irrelevant stimulus is S-R inconsistent, the irrelevant stimulus unit activates the incorrect response unit, but feeds negative input to the response unit that is being activated by the controlled line. As a result, activation in the correct response unit accumulates faster for the S-R consistent condition than the S-R inconsistent condition.
Activation in the response units continues until the activation level in a response unit reaches the response threshold, and a response is selected and executed.
The shape of the irrelevant stimulus activation curve allows the computational model to account not only for the basic raw effects of all of the compatibility tasks in the dimensional overlap taxonomy, but also the time-courses of the effects that appear when the irrelevant stimulus is presented at different intervals before or after the relevant stimulus (see Kornblum et al. 1999).
Now that you have been introduced to the overall theory of the model, you may want to try it out for yourself! You can play with a fully functioning online implementation of the model, adjusting parameters and seeing the results for different types of consistency tasks.