A connectionist approach to processing dimensional interaction
The difference between integral and separable interaction of dimensions is a classic problem in cognitive psychology (Garner 1970, American Psychologist, 25: 350-358, Shepard 1964, Journal of Mathematical Psychology, 1: 54-87) and remains an essential component of most current experimental and theoretical analyses of category learning (e. g. Ashby and Maddox 1994, Journal of Mathematical Psychology, 38: 423-466, Goldstone 1994, Journal of Experimental Psychology: General, 123: 178-200, Kruschke 1993, Connection Science, 5: 3-36, Melara et al. 1993, Journal of Experimental Psychology: Human Perception & Performance, 19: 1082-1104, Nosofsky 1992, Multidimensional Models of Perception and Cognition, Hillsdale NJ: Lawrence Erlbaum). So far the problem has been addressed through post hoc analysis in which empirical evidence of integral and separable processing is used to fit human data, showing how the impact of a pair of dimensions interacting in an integral or a separable manner enters into later learning processes. In this paper, we argue that a mechanistic connectionist explanation for variations in dimensional interactions can provide a new perspective through exploration of how similarities between stimuli are transformed from physical to psychological space when learning to identify, discriminate and categorize them. We substantiate this claim by demonstrating how even a standard backpropagation network combined with a simple image-processing Gabor filter component provides limited but clear potential to process monochromatic stimuli that are composed of integral pairs of dimensions differently from monochromatic stimuli that are composed of separable pairs of dimensions. Interestingly, the responses from Gabor filters are shown already to capture most of the dimensional interaction, which in turn can be operated upon by the neural network during a given learning task. In addition, we introduce a basic attention mechanism to backpropagation that gives it the ability to attend selectively to relevant dimensions and illustrate how this serves the model in solving a filtration versus condensation task (Kruschke 1993, Connection Science, 5: 3-36). The model may serve as a starting point in characterizing the general properties of the human perceptual system that causes some pairs of physical dimensions to be treated as integrally interacting and other pairs as separable. An improved understanding of these properties will aid studies in perceptual and category learning, selective attention effects and influences of higher cognitive processes on initial perceptual representations.
gabor filters integral and separable dimensions connectionism