Translation versus rotation as dominant training input feature.

<p>Every plot group visualizes a different aspect of the trained SFA units and within each plot group, nine units are shown (every third, starting from the first, up to SFA unit number 25). Columns from left to right: optimal excitatory stimuli, orientation/phase response, response in Fourier space, orientation tuning plots. Rows: <b>A</b> SFA units trained with pink noise images that were subject to translation only. <b>B</b> Units trained with a mixture of rotation and translation. <b>C</b> Units trained with input that contained rotation only.</p

Response of the SFA units as a function of orientation of sinusoidal gratings.

<p><b>A</b> SFA unit response as a function of orientation. Solid red (dashed blue) lines indicate excitatory (inhibitory) response. <b>B</b> Orientation tuning functions of V1 cells of macaque monkey (figure adapted from DeValois et al. (1982) <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003564#pcbi.1003564-DeValois1" target="_blank">[55]</a>). Note that inhibitory effects were not investigated by DeValois et al. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003564#pcbi.1003564-DeValois1" target="_blank">[55]</a>, and thus there are no inhibitory responses plotted in <b>B</b>.</p

Polar plot of frequency tuning and orientation of the filters learned on whitened natural image patches.

<p>(a) for a GRBM-196-196 and (b) for a GRBM-196-588. The crosshairs describe the selectivity of the filters, which is given by the 1/16-bandwidth in spatial-frequency and orientation, see [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171015#pone.0171015.ref038" target="_blank">38</a>] for details.</p

Comparison of for different models trained on the blind source separation task.

<p>Comparison of for different models trained on the blind source separation task.</p

Recall performance of the model with random input.

<p>Performance in CA3 (left column) and in EC (right column). <b>A-B</b>: Recall performance in CA3 and EC; dashed lines are simulations without recurrent connections. <b>C-D</b>: Proportion of correctly retrieved cues. Left side in inset of <b>C</b> illustrates that the cue (star) is retrieved correctly. The reconstruction is most correlated with corresponding stored pattern (star) compared to the other stored pattern (moon and sun). Right side shows when cue is confused with another stored pattern. Here the reconstruction is more correlated with the sun than with the star. Coloured bars explain code in <b>E-H</b>. <b>E-F</b>: Histogram of pairwise correlations between reconstructed pattern and corresponding stored pattern (cyan, blue) and between reconstructed pattern and another stored pattern (red). Blue indicate the cases when the correlation between the reconstructed pattern and the stored pattern is not maximal. Star marks mean of the distribution of the correlation between the reconstructed pattern and the stored pattern. The histogram is calculated at the cue quality indicated by the red rhombus in <b>A-D</b>. <b>G-H</b>: Same as <b>E-F</b> but with recurrent connections enabled.</p

Sums of the mixing coefficients for models trained on the blind source separation task.

<p>Sums of the mixing coefficients for models trained on the blind source separation task.</p

Relation between the EPSP and the Learning Window

<p>The power spectrum is the Fourier transform of the effective learning window <i>W</i>₀, which in turn is the convolution of the learning window <i>W</i> and the EPSP <i>ε</i>. The figure shows the learning windows required for SFA for three different EPSP durations (<i>τ</i> = 4, 40, 400 ms). The maximal input frequency <i>ν</i>_max was 1 / (40 ms) in all plots. </p

Slow Feature Analysis on Retinal Waves Leads to V1 Complex Cells

<div><p>The developing visual system of many mammalian species is partially structured and organized even before the onset of vision. Spontaneous neural activity, which spreads in waves across the retina, has been suggested to play a major role in these prenatal structuring processes. Recently, it has been shown that when employing an efficient coding strategy, such as sparse coding, these retinal activity patterns lead to basis functions that resemble optimal stimuli of simple cells in primary visual cortex (V1). Here we present the results of applying a coding strategy that optimizes for temporal slowness, namely Slow Feature Analysis (SFA), to a biologically plausible model of retinal waves. Previously, SFA has been successfully applied to model parts of the visual system, most notably in reproducing a rich set of complex-cell features by training SFA with quasi-natural image sequences. In the present work, we obtain SFA units that share a number of properties with cortical complex-cells by training on simulated retinal waves. The emergence of two distinct properties of the SFA units (phase invariance and orientation tuning) is thoroughly investigated via control experiments and mathematical analysis of the input-output functions found by SFA. The results support the idea that retinal waves share relevant temporal and spatial properties with natural visual input. Hence, retinal waves seem suitable training stimuli to learn invariances and thereby shape the developing early visual system such that it is best prepared for coding input from the natural world.</p></div

Histogram of the number of activated hidden units of a GRBM-196-196.

<p>The model was trained on whitened natural image patches. The histograms before and after training are plotted in blue (dotted) and in green (solid), respectively.</p

Orientation selectivity index (OSI) histograms of SFA units trained with different types of stimuli.

<p><b>A</b> Training with pink noise images that were translated only. <b>B</b> Training with pink noise images that were rotated and translated. <b>C</b> OSI distribution of the Gabor-QFP model. <b>D</b> Training with retinal wave image sequences. Histograms in <b>A</b>, <b>B</b>, and <b>D</b> were obtained by pooling OSI values from the first 50 SFA units of 10 simulation runs with identical parameters for the training input generation.</p