Computational Models for Generic Cortical Microcircuits - Computational Neuroscience: A Comprehensive Approach - page 582

not be for another (see for example Figure 18.2) , indicating that equivalence classes
and dynamic stability exist purely from the perspective of the readout elements.

18.5.2 Predicting movements and solving the aperture problem

This section reports results of joint work with Robert Legenstein [13], [18]. The
general setup of this simulated vision task is illustrated in Figure 18.6. Moving
objects, a ball or a bar, are presented to an 8 x 8 array of sensors (panel a). The
time course of activations of 8 randomly selected sensors, resulting from a typical
movement of the ball, is shown in panel b. Corresponding functions of time, but
for all 64 sensors, are projected as 64 dimensional input by a topographic map into
a generic recurrent circuit of spiking neurons. This circuit with randomly chosen
sparse connections had been chosen in the same way as the circuits for the preceding
tasks, except that it was somewhat larger (768 neurons) to accommodate the 64 input
channels.A16x16x3neuronalsheetwasdividedinto642x2x3input regions.
Each sensor injected input into 60 % randomly chosen neurons in the associated
input region. Together they formed a topographic map for the 8 x 8 array of sensors.
The resulting firing activity of all 768 integrate-and-fire neurons in the recurrent
circuit is shown in panel c. Panel d of Figure 18.6 shows the target output for 8 of
the 102 readout pools. These 8 readout pools have the task to predict the output that
the 8 sensors shown in panel b will produce 50 ms later. Hence their target output
(dashed line) is formally the same function as shown in panel b, but shifted by 50
ms to the left. The solid lines in panel d show the actual output of the corresponding
readout pools after unsupervised learning. Thus in each row of panel d the difference
between the dashed and predicted line is the prediction error of the corresponding
readout pool.
The diversity of object movements that are presented to the 64 sensors is indicated
in Figure 18.7 . Any straight line that crosses the marked horizontal or vertical line
segments of length 4 in the middle of the 8 x 8 field may occur as trajectory for the
center of an object. Training and test examples are drawn randomly from this - in
principle infinite - set of trajectories, each with a movement speed that was drawn
independently from a uniform distribution over the interval from 30 to 50 units per
second (unit = side length of a unit square). Shown in Figure 18.7 are 20 trajectories
that were randomly drawn from this distribution. Any such movement is carried out
by an independently drawn object type (ball or bar), where bars were assumed to be
oriented vertically to their direction of movement. Besides movements on straight
lines one could train the same circuit just as well for predicting nonlinear movements,
since nothing in the circuit was specialized for predicting linear movements.
Thirty-six readout pools were trained to predict for any such object movement
thesensoractivationsofthe6x6sensorsintheinteriorofthe8x8array25ms
into the future. Further 36 readout pools were independently trained to predict their
activation 50 ms into the future, showing that the prediction span can basically be
chosen arbitrarily. At any time t (sampled every 25 ms from 0 to 400 ms) one uses for
each of the 72 readout pools that predict sensory input E T into the future the actual
activation of the corresponding sensor at time t + E T as target value ( correction )for