Abstract
Many research questions in vision involve determining whether stimulus properties are processed independently in visual cortex. Unfortunately, most previous research has only vaguely defined what is meant by “independence,” which hinders its precise quantification and testing. Here, we develop a new framework that links general recognition theory from psychophysics and encoding models from computational neuroscience. We focus on separability, a form of independence equivalent to the concept of “invariance” often used in vision science. This new framework allows us to precisely define separability of neural representations and to theoretically link such definition to psychophysical and neuroimaging tests of independence and invariance. In particular, the theory identifies exactly what valid inferences can be made about independent encoding of stimulus dimensions from the results of multivariate analyses of neuroimaging data. In addition, two commonly used operational tests of independence are re-interpreted within this new theoretical framework, providing insights on their correct use and interpretation. We validated this extended general recognition theory in an fMRI study involving gratings varying in orientation and spatial position. Participants completed 4 two-hour sessions in the MRI scanner, in which they were presented with oriented gratings varying in orientation in 45-degree steps (0, 45, 90, and 135 degrees) while they fixated to the center of the screen. Stimuli were presented in 3 different spatial positions in the visual field. The known features of receptive fields in the primary visual cortex led us to expect that changing the position of stimuli should systematically change encoding separability of orientation, with lower separability for stimuli positioned farther apart. Our results show that decoding tests developed within the proposed framework can validly detect failures of encoding separability, but decoding tests in general (including tests in the literature) cannot validly detect presence of encoding separability, or “invariance,” without producing false positives.