Linear-nonlinear (LN) models and their extensions have proven successful in describing transformations from stimuli to spiking responses of neurons in early stages of sensory hierarchies. Neural responses at later stages are highly nonlinear and have generally been better characterized in terms of their decoding performance on prespecified tasks. Here we develop a biologically plausible decoding model for classification tasks, that we refer to as neural quadratic discriminant analysis (nQDA). Specifically, we reformulate an optimal quadratic classifier as an LN-LN computation, analogous to “subunit” encoding models that have been used to describe responses in retina and primary visual cortex. We propose a physiological mechanism by which the parameters of the nQDA classifier could be optimized, using a supervised variant of a Hebbian learning rule. As an example of its applicability, we show that nQDA provides a better account than many comparable alternatives for the transformation between neural representations in two high-level brain areas recorded as monkeys performed a visual delayed-match-to-sample task

We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli that are nongaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high-dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. Existing analysis methods are based on correlation functions between stimuli and responses, but these methods are guaranteed to work only in the case of gaussian stimulus ensembles. As an alternative to correlation functions, we maximize the mutual information between the neural responses and projections of the stimulus onto low-dimensional subspaces. The procedure can be done iteratively by increasing the dimensionality of this subspace. Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. If the dimensionality of the relevant subspace indeed is small, it becomes feasible to map the neuron's input-output function even under fully natural stimulus conditions. These ideas are illustrated in simulations on model visual and auditory neurons responding to natural scenes and sounds, respectively.