The information propagation problem.

<p>This problem is illustrated with the visual periphery, but the information propagation problem is general: it arises whenever information is transmitted from one area to another, and also when information is combined to carry out computations. (<b>A</b>) The retina transmits information about visual stimuli, <i>s</i>, to the visual cortex. The information does not propagate directly from retina to cortex; it is transmitted via an intermediary structure, the lateral geniculate nucleus (LGN). Consequently, the information about the stimuli that is available to the cortex, denoted <i>I</i>_<i>y</i>(<i>s</i>), is not the same as the information that retina transmits, denoted <i>I</i>_<i>x</i>(<i>s</i>). Here, we ask what properties of neural activities in the periphery maximize the information that propagates to the deeper neural structures. (<b>B</b>) Illustration of our model. Neural activity in the periphery, <b>x</b>, is generated by passing the stimulus, <i>s</i>, through a set of neural tuning curves, <b>f</b>(<i>s</i>), and then adding zero-mean noise, <b><i>ξ</i></b>, which may be correlated between cells. This activity then propagates via feed-forward connectivity, described by the matrix <b>W</b>, to the next layer. The activity at the next layer, <b>y</b>, is generated by passing the inputs, <b>W</b> · <b>x</b>, through a nonlinearity <i>g</i>(⋅), and then adding zero-mean noise, <b><i>η</i></b>.