How Does Perceptual Discriminability Relate to Neuronal Receptive Fields?

Perception is an outcome of neuronal computations. Our perception changes only when the underlying neuronal responses change. Because visual neurons preferentially respond to adjustments in some pixel values of an image more than others, our perception has greater sensitivity in detecting change to some pixel combinations more than others. Here, we examined how perceptual discriminability varies to arbitrary image perturbations assuming different models of neuronal responses. In particular, we investigated that under the assumption of different neuronal computations, how perceptual discriminability relates to neuronal receptive fields – the change in pixel combinations that invokes the largest increase in neuronal responses. We assumed that perceptual discriminability reflects the magnitude of change (the L2 norm) in neuronal responses, and the L2 norm assumption gained empirical support. We examined how perceptual discriminability relates to deterministic and stochastic neuronal computations. In the case of deterministic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields. For multiple layers of canonical linear-nonlinear (LN) computations in particular (which is a feed-forward neural network), neuronal receptive fields are linear transforms of the first-layer neurons’ image filters. When one image is presented to the neural network, the first-layer neurons’ filters and the linear transform completely determine neuronal receptive fields across all layers, and perceptual discriminability to arbitrary distortions to the image. We expanded our analysis to examine stochastic neuronal computations, in which case perceptual discriminability can be summarized as the magnitude of change in stochastic neuronal responses, with the L2 norm being replaced by a Fisher-information computation. Using a practical lower bound on Fisher information, we showed that for stochastic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields, together with how responses co-variate across neurons.