The influence of the place-value structure of the Arabic number ...

advantages for these numbers (see above for a discussion). Then these numbers were split into
their decade and unit digits. On the basis of these single digits the respective input pattern was
computed. Then, the net activation of the hidden layer was determined. The hyperbolic
tangent of this net weight was then used as the actual activation. The output function of the
hidden layer was the identity function. The net activation of the output nodes was again
computed by formula (1) with the hyperbolic tangent as the activation function. This was
repeated until (i) the activation of one of the output nodes exceeded the threshold or (ii) the
time limit was reached 1 . The actual output was then calculated using formula (2). Finally, the
back propagation learning algorithm was applied meaning that the connection weights were
adjusted on the basis of the difference between the activation of the output and the hidden
layer of the network model.
The network model representing the holistic model was trained quite similarly, however,
without breaking up the numbers presented into tens and unit digits. Nevertheless, as in this
model the hidden as well as the output layer would consist of two nodes connected by an
identity function (which would not alter the connection weights) no hidden layer was realized
in this model. Thus, the holistic computational model comprised an input and an output layer
only. Thereby, just one matrix of weights had to be learned, following the delta rule approach.
MODEL PERFORMANCE
For the case of brevity the way the connection weights developed while training the
models will not be illustrated in the main text of this article. Nevertheless, for the interested
reader Appendix B provides a detailed description of the development of the connection
weights for each of the three models.
1 Please note that for each of the three models the mean of the simulated RTs was more than 4 standard
deviations from the upper time limit indicating that in the vast majority of trials a the neural network models
had come to a decision far before the time limit was reached.
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