One of the basic assumptions shared by all connectionist models of reaction time is that mental codes form gradually, through the accumulation of evidence over time based on input information. For example, when a blue stimulus appears, information from the sensory signals gradually causes evidence to accumulate in favor of the stimulus code representing the color blue. In the language of connectionist networks, the activation of the stimulus unit for the color blue gradually increases over time. A mental code can be thought of as “completely formed” once activation in the appropriate unit has reached some criterion level. Activation in a stimulus unit can trigger the accumulation of activation in a response unit either right away, or after a decision threshold is met, depending on whether the model assumes stages or continuous processing. The ultimate speed of performance is determined by how long it takes for activation of the motor units to reach some “decision criterion,” indicating that the motor codes have been fully formed.
This idea evolved out of the combination of three ideas. Signal detection theory (Green & Swets, 1966; Swets, 1964; Tanner & Swets, 1954) suggested that detecting a particular stimulus (i.e. forming a particular stimulus code) is a statistical decision: the signals that you get from your sensory system are subject to variability, so although a particular stimulus characteristic on average produces a particular sensory signal, there will be times when the signal appears without the stimulus being there, and there will be times when the signal fails to appear when the stimulus is there. So, you have to use a decision threshold for how strong the signal has to be so that you are most likely to detect it when it is there, but least likely to think it is there when it is actually not.
Stimulus sampling theory (Estes, 1950, 1955) introduced the idea that perception involves repeated sampling of a stimulus over time, allowing signal detection theory to be extended over time (see, e.g., Pike, 1973). The statistical decision tool called sequential sampling and optional stopping (Wald, 1947) is used whenever you do not want to sample more data than necessary, to determine the number of times a signal has to be sampled in order to make a confident decision about its value. According to this method, each additional sample of information modifies your cumulative level of confidence, allowing you to continue sampling information until your confidence is high enough to meet some decision criterion, at which point you stop sampling.
This idea was immediately incorporated into a large number of psychological models of performance in CRT tasks (e.g. Audley, 1960; Audley & Pike, 1965; LaBerge, 1962; McGill, 1963, 1967; Stone, 1960; Vicker, 1970). Although the details of these models differ, the basic premise is the same: evidence for each stimulus code accumulates over time, due to repeated sampling of sensory information, until a decision criterion of some sort is reached, indicating that the code has been fully formed and the stimulus has therefore been fully identified (see Luce, 1986, for more details). Currently, two major types of models based on this premise are being pursued: diffusion models (Ratcliff, 1978, 1980, 1981, 1988) and the connectionist models discussed here.
Most connectionist models use the same equation to determine how activation changes over time, drawing on the first connectionist model of performance, McClelland’s (1979) Cascade model. McClelland proposed that units be understood as first-order linear integrators, so that their activation at any given point in time is a time-averaging function of their input. When units like this are given a constant input, their activation will asymptotically approach that input value according to a “loading curve”: approaching the input level at a rate proportional to how far away it is from the input. This function actually first appeared in a psychological model proposed by Grice (1972, 1977; Grice, Nullmeyer, & Spiker, 1982), although he rarely gets credit for this contribution (see Luce, 1986).