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

Decomposed model
The connection weights of the two numbers (from the input to the hidden layer) as
well as those for tens and units (from the hidden to the output layer) developed in
diametrically opposed ways as described for the holistic model. Moreover, for the connection
from the input to the hidden layer the connection weight pattern for decade and unit digits did
not have a linear slope. Instead, as already observed in the model by Verguts et al. (2005) the
pattern is described best by a compressed function as generally, differences between the
connection weights of two successive numbers are larger for relatively smaller numbers (i.e.,
2_3 vs. 7_8). According to Verguts and colleagues (2005) this pattern is determined by the
frequency distribution of the single digits (i.e., 1 - 9) used for training the model, rather than
allowing any kind of inferences on the scaling properties (i.e., logarithmic vs. linear) of the
underlying magnitude representation. Importantly, in the present simulations the connection
weights for the decade digits were stronger than the weights for the unit digits (with the
difference between the minimum and maximum weight being about three times larger for the
connection weights of the decade digits, see Figure C); thereby suggesting a more prominent
influence of the decade digits in two-digit number magnitude comparison. This mirrors results
repeatedly observed in regression analyses on empirical RT data. Here, the beta weights of for
the predictor decade distance (when considered in the final model) were found to be two to
four times higher than the beta weights for the unit distance (e.g., Knops, 2006; see Nuerk &
Willmes, 2005 for a discussion).
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