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 ofthe 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 back-propagation 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.

A common misperception within the neural network community is that even with nonlinearities in their hidden layer, autoassociators trained with backpropagation are equivalent to linear methods such as principal component analysis (PCA). Our purpose is to demonstrate that nonlinear autoassociators actually behave differently from linear methods and that they can outperform these methods when used for latent extraction, projection, and classification. While linear autoassociators emulate PCA, and thus exhibit a flat or unimodal reconstruction error surface, autoassociators with nonlinearities in their hidden layer learn domains by building error reconstruction surfaces that, depending on the task, contain multiple local valleys. This interpolation bias allows nonlinear autoassociators to represent appropriate classifications of nonlinear multimodal domains, in contrast to linear autoassociators, which are inappropriate for such tasks. In fact, autoassociators with hidden unit nonlinearities can be shown to perform nonlinear classification and nonlinear recognition.

We describe a new adaptive network model, the consequential region model, for the identification and categorization of stimuli varying on multiple, continuous dimensions. If the dimensions are binary-valued, the model reduces to Gluck's (1991; Gluck Gf Bower, 1988a) configural-cue model. The consequential region model attempts to provide an adaptive network mechanism to approximate the computations of the multidimensional-scaling choice model (identification) and the generalized context model (categorization). We begin by describing the architecture of the model and the scheme by which stimuli are represented within it. This scheme is motivated by Shepard's (1987) analysis of stimulus generalization and Gluck's (1991) extension of that analysis to network theories of animal and human learning. The main part of the paper describes five simulation experiments in which we attempted to fit the model to identification and categorization data reported by Nosofsky (1987) and Nosofsky et al. (1989), as well as to some artificial identification data. Nosofsky's (1987) stimuli were Munsell color patches varying in brightness and saturation, which are known to be integral dimensions. Nosofsky et al.'s (1989) stimuli, on the other hand, varied on separable dimensions. The model is able to provide excellent fits to the identification and categorization results, including learning.and transfer data. Our results illustrate how an associative network can show appropriate sensitivity to inter-item similarities among training exemplars as an emergent property of its scheme for representing stimuli.