Academic journal article Psychonomic Bulletin & Review

Merging Race Models and Adaptive Networks: A Parallel Race Network

Academic journal article Psychonomic Bulletin & Review

Merging Race Models and Adaptive Networks: A Parallel Race Network

Article excerpt

This article presents a generalization of race models involving multiple channels. The major contribution of this article is the implementation of a learning rule that enables networks based on such a parallel race model to learn stimulus-response associations. This model is called a parallel race network. Surprisingly, with a two-layer architecture, a parallel race network learns the XOR problem without the benefit of hidden units. The model described here can be seen as a reduction-of-information system (Haider & Frensch, 1996). An emergent property of this model is seriality: In some conditions, responses are performed with a fixed order, although the system is parallel. The mere existence of this supervised network demonstrates that networks can perform cognitive processes without the weighted sum metric that characterizes strength-based networks.

The objective of this article is to expand our knowledge of race models by showing the existing similarities between race models and connectionist networks. To this end, the architecture of race models is extended into the form of a network of connections, and a learning rule is introduced whose purpose is similar to the delta rule (Widrow & Hoff, 1960). With such a common denominator, race models and connectionist models will, for the first time, be comparable. In this article, I introduce this integration of race and network approaches in the form of a parallel race network (PRN) model. One feature that is introduced in this network is redundancy of channels. Redundancy might be an important aspect of the human brain and, thus, should be considered when a network model of the brain is presented.

Overview of the Single-Channel Race Models

Accumulator models and random walk models are generalizations of the signal detection theory (SDT), sharing the same core assumption: One or many samples are sequentially received from the senses (Green & Swets, 1966). However, contrary to SDT, accumulator models and random walk models can take an arbitrary number of samples, this number changing from trial to trial. In these models, the samples can be evidence for one response or an alternative response (Townsend & Ashby, 1983). In some variants, the samples can also be evidence for both responses or neither. Following Smith and Vickers (1988), the distinction between random walks and accumulator models lies in the nature of the evidence accumulation process. For the former, the accumulation process is not independent, because an evidence for one response implies a reduction of the amount of evidence for the alternative response. For the latter, the evidence accumulations are done on independent accumulators. However, the first accumulator filled triggers a response-thus, the name of race model.

The class of accumulator models can be further broken down by whether the evidence collected is discrete, called simple accumulator models by Luce ( 1986), or continuous, called strength accumulator models (Laberge, 1962). Examples of simple accumulator models are given by Audley and Pike (1965), where the sampling process takes a fixed amount of time, and by Pike (1973), where the time between two samples is continuous. An example of a strength accumulator is given by Smith and Vickers (1988), where the time between two samples is fixed. Another distinction between race models is whether the channels bringing evidence to the accumulator are dependent or independent (Meijers & Eijkman, 1977).

All these models share one limitation: The evidence must travel sequentially through a single channel. As a result of this constrained architecture, the accumulators are located after a bottleneck. Yet, as has been noted by Thorpe and Gautrais ( 1999), there might not be enough time for information jam. These authors "recently demonstrated that the human visual system can process previously unseen natural images in under 150 ms . . . To reach the temporal lobe in this time, information from the retina has to pass through roughly ten processing stages. …

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