Abstract
Many research questions in vision science involve determining whether stimulus properties are represented and processed independently in the brain. 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 special form of independence that is equivalent to the concept of “invariance” often used by vision scientists, but we show that other types of independence can be formally defined within the theory. We show how 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. The framework formally specifies the relation between these different levels of perceptual and brain representation, providing the tools for a truly integrative research approach. 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. Finally, we discuss the results of an fMRI study used to validate and compare several tests of representational invariance, and confirm that the relations among them proposed by the theory are correct.