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In-Depth Information
2.5
Evaluation of the Adaptive Learning Rate
To evaluate the adaptive learning rate proposed in Sec. 2.1, artificial 1-D test data of
length
T
=11
in the interval
[
−
π
;
π
[
is generated using the following equations:
x
= sin(
t
)
,
(9)
x
=
sin(3
t
)
·
sin(
t
)
−
0
.
5
.
(10)
2
t
2
Eq. 9 is referred to as
sin
and Eq. 10 as
sinc
. Except for the following differences, the
RNNPB network parameters were identical to the parameters of the robot experiments
(see below). The architecture contained only one input and one output node, as well as
only one PB unit. The convergence criterion was set to
10
−
4
.
2.6
Network Parameters for Robot Experiments
Based on systematic empirical trials, the following parameters have been determined
for our experiments. The network contained two input and two output nodes, 24 hid-
den and 24 context neurons as well as 2 PB units. The convergence criterion for back
propagation through time (BPTT) was set to
10
−
6
in the first, and
10
−
5
in the second
experiment. For recognition of a sequence, the update rate
γ
of the PB values was set to
0.1. The values for all other individual adaptive learning rates (Eq. 5) during training of
the synaptic weights were allowed to be in the range of
η
min
=10
−
12
and
η
max
=50
;
depending on the gradient they were either increased by
ξ
+
=1
.
01
or decreased by a
factor
ξ
−
=0
.
9
.
3
Scenario
The humanoid robot Nao
1
is programmed to conduct the experiments (Fig. 3 a). The
task for the robot is to identify which object (toy brick) it holds in its hand. In total
there are eight object categories that have to be distinguished by the robot: the toy bricks
have four different shapes (circular-, star-, rectangular- and triangular-shaped), of which
each exists in two different weight versions (light and heavy). Hence, for achieving a
successful classification multi-modal sensory impressions are required. Additionally,
active
perception is necessary to induce sensory changes essential for discrimination of
-depending on the perspective- similar looking shapes (e.g. star- and circular-shaped
objects). For this purpose, the robot performs a predefined motor sequence and simul-
taneously acquires visual and proprioceptive sensor values.
3.1
Data Acquisition
The recorded time series comprises 14 sensor values for each modality. In each single
trial the robot turns its wrist with the object between its fingers by 45.8
◦
back and forth
