Quadratic ideal
observation and recurrent preprocessing in perceptual
learning
Li Zhaoping     Michael H Herzog    
Peter Dayan
Network 14, 233-247.
Abstract
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.
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