Applying an exemplar model to the serial reaction-time task: Anticipating from experience

Abstract

We present a serial reaction time (SRT) task in which participants identified the location of a target by pressing a key mapped to the location. The location of successive targets was determined by the rules of a grammar, and we varied the redundancy of the grammar. Increasing both practice and the redundancy of the grammar reduced response time, but the participants were unable to describe the grammar. Such results are usually discussed as examples of implicit learning. Instead, we treat performance in terms of retrieval from a multitrace memory. In our account, after each trial, participants store a trace comprising the current stimulus, the response associated with it, and the context provided by the immediately preceding response. When a target is presented, it is used as a prompt to retrieve the response mapped to it. As participants practise the task, the redundancy of the series helps point to the correct response and, thereby, speeds retrieval of the response. The model captured performance in the experiment and in classic SRT studies from the literature. Its success shows that the SRT task can be understood in terms of retrieval from memory without implying implicit learning.

Keywords:

• Artificial grammar
• Serial response-time task
• Global memory model
• Implicit learning
• Hick–Hyman Law

The research was supported by grants from the Natural Sciences and Engineering Research Council of Canada to both authors. We thank Joaquin Vaquero, Beth Johns, Bill Hockley, Scott Brown, Denis Cousineau, Matthew Kelly, and Ben Murdock for comments on a draft of the paper.

Notes

¹ Although the judgement-of-grammaticality task has been used widely to investigate implicit learning, it lacks precision. First, it is unclear exactly what information a participant uses to make the choice. Second, a binary judgement truncates information into two categories: unlikely to do justice to subtle details in whatever has been learned. Third, decisions about test strings' grammaticality are collected after a study phase; it is not clear how loss of information between acquisition and test will affect those decisions. Finally, the grammars explored in many experiments conflate stimulus properties including positional dependencies (e.g., strings can begin with only one or two symbols), sequential dependencies (e.g., each letter can be followed by only one or two others), string length, the frequency of repeated letters, and so forth. Conflating so many factors makes a clear analysis difficult (see Johnstone & Shanks, 1999, 2001, for a full discussion).

² For an example with a number of equally likely stimuli, uncertainty, U, is computed as,

where N is the number of stimulus alternatives, and p = 1/N is the probability that each alternative will occur on a given trial. U is expressed in bits. To calculate mean uncertainty when the probabilities of events are unequal, the uncertainty of each event is weighted by its probability, and the product is summed across all events—that is,

where N refers to the number of events, and p _i is the probability of event i (see Shannon & Weaver, 1949).

³ Orthogonal trend coefficients for unequal intervals were computed using an algorithm suggested by Gaito (1965). Software to compute the coefficients is available from the authors for Linux, Solaris, Macintosh-Intel, or 32-bit Windows machines.

⁴ In our simulations, we have limited the context information to the immediately preceding response. The decision to limit the context was one of convenience; we are open to the possibility that a larger context might be required if second-, third-, or higher order predictability were introduced into a sequence of stimuli (cf. Reed & Johnson, 1994; Remillard, 2008).

⁵ Minerva 2 has a mechanism, called deblurring, in which the echo retrieved is fed iteratively back into the system until the response subtrace is clear enough to support a response. We tried to model performance with this mechanism but failed. Indeed, as we increased the number of traces studied, when deblurring, the response subtrace became increasingly noisy rather than becoming increasingly clear. Dienes (1992) reported the same problem.

⁶ The IRM, described by Mewhort and Johns (2005), set the exponent on the initial time step to 0 and increased it by 1 on each iteration; this differs from our practice of setting the initial time step to 1 and increasing it by 1 on each iteration. Their vectors were composed of zeros and ones; ours were composed of − 1s and + 1s.

⁷ The model has only two free parameters—namely, L, the encoding quality parameter, and k, the decision criterion. The encoding parameter, L, controls the quality of the representation in memory. If it is set to 1, learning is speeded: In Experiment 1, for example, learning would be all but complete within the first block of trials. If it is set to a low value, the rate of learning is strongly attenuated. Its influence is greatest for the low-redundancy sequences. The decision criterion, k, controls the quality of information retrieved needed to issue a decision. Decreasing the decision criterion speeds response time but increases the probability of an error response. If the decision criterion is set to a very low value, accuracy suffers accordingly. In addition to the free parameters, the model has a structural parameter—namely, the dimensionality of the vectors that represent each symbol. Decreasing the dimensionality both reduces the rate of learning and increases the number of errors. The dimensionality parameter trades off with L, and all three parameters interact. We selected parameter values so that the same values work in all the simulations. We could have modestly better fits to each task, but we have little justification for changing the parameters across tasks.

⁸ There is an error in Hyman's (1953) figure. The panel for participant L.S. shows nine data points for Experiment 2 and seven for Experiment 1. The data point at U = 2.81 bits for Experiment 2 should be attributed to Experiment 1. We fixed the error in Figure 7.

⁹ Others have argued that Hick's results reflect a strategy based on a speed–accuracy trade-off (Fitts, 1966; see also Fitts & Posner, 1967). Because the chance of a response error increases with the number of response alternatives and because the participants were given opportunity to note the number of alternatives, they may have delayed their response conditional on the number of alternatives to ensure that they respond correctly. Usher, Olami, and McLelland (2002) have worked out the details of the trade-off idea in the context of a diffusion-based information accumulation model (see Brown & Heathcote, 2005, for a review of information accumulation models). Although their account handles Hick's data successfully, the trade-off idea has no way to anticipate changes in RT based on sequential dependencies, as in Hyman's data. To make the trade-off idea work for Hyman's task, one would have to suppose that participants adjust response times conditional on sequential dependencies. The problem is that there are no cues to the dependencies equivalent the number of alternatives in Hick's task. In short, when applied to the Hick–Hyman law, the trade-off idea begs the question. Hence, we see no way that the speed–accuracy trade-off idea could handle Hyman's (1953) demonstration that stimulus uncertainty, not number of stimuli, predicts response latency.