The computational models of task-switching can be broadly classified into normative models and process models. The normative models are models that describe an optimal behaviour under specific theory-driven assumptions, but the behaviours from the model are not grounded by process-based
constraints. A normative model asks: “given a particular theory, what is the optimal level of performance that should be observed?” It does not map real-time behaviours in a given study, and is generally less concerned about the interactions of different processes than a process model. A normative model has clear mathematical specification for each cognitive process.
Meiran's (2000) normative model aimed to understand how inter-trial response conflicts with bivalent response sets give rise to RT cost. In the model, task-associated stimuli and responses each form different mental representations. The RT cost arises because of the similarity/ dissimilarity between the newly calculated response representations and the n-1 response representations. If the representations are similar, then there is a greater response potency than if the two representations are dissimilar. The value of response potency is used to infer how much RT would be slowed. The model focuses on quantifiable interferences between different mental representations, but lacks processes that govern goal activation and maintenance. In contrast, Logan and colleagues’ normative models incorporate different forms of memory retrieval in switching tasks (Logan & Bundesen, 2003; Schneider & Logan, 2005). These authors developed different models reflecting different theoretical assumptions—a model that assumed slow retrieval of task cue from long-term memory (i.e. endogenous control), and a model that assumed a fast priming function from short-term memory. Each cognitive process is governed by specific mathematical equations. They found that performance predicted by the priming model fitted the participant’s data better than the model with endogenous control, and concluded that RT switch costs were largely attributable to interferences. In all, these normative models are concerned with
a specific aspect of the information process in task-switching studies, and generally do not consider effects from parallel processes.
In contrast, process models incorporate multiple processes within the model, and the computations are carried out in time. Notable process-based models for task-switching include (1) Altmann and Gray's (2008) Cognitive Control Model (CCM), which is an activation based production system model implemented in the ACT-R system (Anderson, 1996), (2) Brown et al.'s (2007) conflict control model, and (3) Gilbert and Shallice 's (2002) interactive activation model. Both latter two models were connectionist models.
Altmann and Gray's (2008) CCM model simulated a sequence of distinct cognitive processes. The model relied on symbolic representations, such as symbolic memories (‘Odd’) and production rules (e.g. ‘retrieve task goal’). The retrieval of memories and the implementation of production rules are governed by mathematically-based activation functions. These activation functions allowed the network to produce non-linear behaviours since multiple symbolic representations could receive activation at a given time point, and thus the production rules did not necessarily follow a strict sequence. For example, in task-switching, the triggering of a task goal (e.g. parity) will send activations to the associated task concepts (e.g. to even-odd), which in turn will send activations to the associated stimulus (even or odd) and responses (e.g. left or right). Although a wrong production rule can be triggered due to the spread of activations across multiple associated representations, the system overall relies on sequential executions of production rules, in the form of ‘if-then’ structure.
Thus, the model embodies many assumptions on the specificity and time course of each production rule. Finally, although parallel spreading activation is allowed in the model, only one production rule is triggered at one time.
In contrast to the production system process models, Brown, Reynolds, and Braver (2007) constructed a multi-module, multi-layer connectionist model for conflict control, with relatively complex firing thresholds and decay functions for the units in each layer (Fig. 1.2). The network architecture is modular with distinct processing layers corresponding to different cortical structure—a perceptual layer, hidden layer, prefrontal cortex layer (PFC), multiple types of anterior cingulate cortex (ACC) layer, output layer and so on. The model simulated letter/number classification tasks, as in Rogers and Monsell's (1995) study, in which the participants were pre-cued to classify a letter-digit compound (e.g. ‘X9’) either by parity of the digit, or by the consonant/vowel of the letter, using overlapping response sets. The model fractionated ACC into distinct functions represented by different processing layers. The model focused on the effects of these ACC-associated layers in inter-trial conflict control. It could account for not only the n-1 switch effect, but also higher-order effects (e.g. n-2 repetition or n-2 switch effects). However, for the purpose of our studies, which did not measure higher-order inter-trial effects, the model may be unnecessarily complex at this stage of investigation.
Figure 1.2. Schematic illustration of Brown et al.'s (2007) connectionist model
for conflict control. The model comprised multiple modules (e.g. input, cue, prefrontal
cortex, different forms of anterior cingulate cortex function), with feedforward
connections between the processing layers. The figure was adopted from the original
paper by Brown et al.'s (2007).
Gilbert and Shallice’s model offer a simpler and more conceptually parsimonious task-switching model (Gilbert & Shallice, 2002), based on the interactive activation framework developed by McClelland and Rumelhart (1981). The model was designed to simulate switching between a dominant word-naming and a non-dominant colour-naming task using Stroop-based stimuli (Fig. 1.3). This model involved a connectionist network with units and fixed weight connections. As in Brown et al.’s (2007) model, there were distinct
processing layers such as a perceptual input layer, a task encoding layer, and an output layer, but the overall architecture was substantially simpler. The mathematical functions in Gilbert and Shallice’s model were also fairly straight-forward—the units in this model had continuous and accumulative activation values (i.e. each unit is an accumulator of the activations in the associated units), and there was little learning (other than the temporary primes) or representational transformation in the model. In addition to the presence of feedforward connections, as in Brown et al.’s model, there were also lateral inhibition connections between the units in the same processing layer. The purpose of these lateral interactions was to facilitate selection among multiple units (i.e. favouring one unit over the others). A more detailed description of Gilbert and Shallice’s task-switching model will be presented in Chapter 5.
Figure 1.3. Schematic illustration of Gilbert and Shallice’s (2002) connectionist
model for task-switching with colour/word Stroop tasks. The model comprised three
main processing layers (task demand, input, and output). The lateral connections among
units in the task demand and output layer are not shown in the figure. The figure was
adopted from the original paper by Gilbert and Shallice (2002).
Despite the simplicity of the mode’s activation functions and the architecture, many task-switching associated phenomenon were successfully captured by Gilbert and Shallice’s model, such as switch costs and priming effects. The model was also able to reproduce the cost asymmetry observed between competing tasks (i.e. larger switch cost to one task than the other), due to the larger top-down signal to compensate for the weaker non-dominant task, compared to the smaller top-down control for the stronger dominant task. Other forms of asymmetric switch costs were also explored, such as asymmetric costs caused simply by differences in connection weights.
The attraction of Gilbert and Shallice’s model for us is its context-sensitivity. This means that the model can be easily adapted to different experimental contexts, as has recently been done by others (e.g., Cooper et al., 2018; Sexton & Cooper, 2017). Additionally, since the model involves connection weights, it can potentially be adapted to model development since development in a connectionist network normally involves weight changes (Mareschal, 2010). For these reasons, the interactive activation model of task-switching by Gilbert and Shallice will be adapted for the behavioural studies in the current thesis.
1.8 Overview of studies and models presented in the thesis