Nonlinear ideal observation and recurrent preprocessing in perceptual learning.

Residual micro-saccades, tremor and fixation errors imply that, on different trials in visual tasks, stimulus arrays are inevitably presented at different positions on the retina. Positional variation is likely to be specially important for tasks involving visual hyperacuity, because of the severe demands that these tasks impose on spatial resolution. In this paper, we show that small positional variations lead to a structural change in the nature of the ideal observer's solution to a hyperacuity-like visual discrimination task such that the optimal discriminator depends quadratically rather than linearly on noisy neural activities. Motivated by recurrent models of early visual processing, we show how a recurrent preprocessor of the noisy activities can produce outputs which, when passed through a linear discriminator, lead to better discrimination even when the positional variations are much larger than the threshold acuity of the task. Since, psychophysically, hyperacuity typically improves greatly over the course of perceptual learning, we discuss our model in the light of results on the speed and nature of learning.

Local correlations, information redundancy, and sufficient pixel depth in natural images.

A mathematical framework that permits the factorization of a joint probability distribution into its localized components for a two-dimensional array of pixels is presented. The factorization was used to estimate the contribution to mutual information of two- (I2) and three-pixel (I3) luminance correlations for a large ensemble of natural images analyzed at various spatial scales and pixel depths b. It is shown that both I2 and I3 saturate at b approximately 6 bits per pixel. Three-pixel correlations are shown to produce only a marginal increase of information redundancy (4%) over two-pixel correlations (50%). Implications for neural representation in visual cortex are discussed.

Hebbian imprinting and retrieval in oscillatory neural networks.

We introduce a model of generalized Hebbian learning and retrieval in oscillatory neural networks modeling cortical areas such as hippocampus and olfactory cortex. Recent experiments have shown that synaptic plasticity depends on spike timing, especially on synapses from excitatory pyramidal cells, in hippocampus, and in sensory and cerebellar cortex. Here we study how such plasticity can be used to form memories and input representations when the neural dynamics are oscillatory, as is common in the brain (particularly in the hippocampus and olfactory cortex). Learning is assumed to occur in a phase of neural plasticity, in which the network is clamped to external teaching signals. By suitable manipulation of the nonlinearity of the neurons or the oscillation frequencies during learning, the model can be made, in a retrieval phase, either to categorize new inputs or to map them, in a continuous fashion, onto the space spanned by the imprinted patterns. We identify the first of these possibilities with the function of olfactory cortex and the second with the observed response characteristics of place cells in hippocampus. We investigate both kinds of networks analytically and by computer simulations, and we link the models with experimental findings, exploring, in particular, how the spike timing dependence of the synaptic plasticity constrains the computational function of the network and vice versa.