An observer model version of general recognition theory

Many research questions involve determining whether two stimulus properties are represented “independently” or “invariantly” versus “configurally” or “holistically”. General recognition theory (GRT) provides formal definitions of such concepts and dissociates perceptual from decisional forms of independence. Two issues with GRT are (1) the arbitrariness of the dimensional space in which the model is defined, and (2) that it provides insight on whether dimensions interact, but not on how they interact. Here, we link GRT to the linear-nonlinear observer model underlying classification image techniques. This model is defined in a non-arbitrary stimulus space, and facilitates studying how sampling of information from that space (summarized in classification images) contributes to dimensional interactions. We define template separability as a form of independence at the level of the perceptual templates assumed by this model, and link it to perceptual separability from the traditional GRT. Their theoretical relations reveal that some violations of perceptual separability may be due to the stimuli used rather than a property of the observer model. Naturalistic stimuli, such as faces, readily produce patterns of interactivity in a GRT model even when there is no perceptual interaction in the underlying observer model. Stimulus factors can also account for reports of unexpected violations of separability found in the literature (e.g., between line orientation and size). In addition, perceptual separability can be observed even when there is no underlying template separability in the observer model. This means that invariance/separability learning may be the product of adaptive modification of non-invariant representations.