# A Study of OWA Operators Learned in Convolutional Neural Networks
## 6 Results and Discussion
### Number of Operators  
The accuracy results of the second experiment are summarized in Table 3, where the top 5 accuracy of the network, averaged over the 40 repetitions with the same configuration, is shown against the number of learned features \(C_{f}\) introduced in the layer. In this experiment, the sorting metric is the total variation, and \(\alpha\) is set to 128. The final top 5 accuracies are also shown as a violin plot in Figure 3, where we can observe a clear correlation between the increase in \(C_{f}\) and the final top 5 accuracy, with all the results with a \(C_{f}>4\) showing a statistically significant result over the reference. The improvement shown reaches 3% over the reference when the highest number of learned features is used. This suggests that adding more operators also increases the knowledge added to the network and proves the diversity of the operators learned in the training.  
In Figure 4, we show the orness and dispersion profiles of the learned operators, obtained in the same fashion as in Section 6.1. For this figure, considering the variable number of features learned \(C_{f}\), we use a logarithmic horizontal axis to simplify the comparison between different configurations. On the orness profiles, we can observe how, for each number of features \(C_{f}\) from 2 to 16, an increase in the number of features implies an increase in the range of orness. In those cases the upper limit of the profile is close to 1.0 (_max_-like), while the lower limit begins at 0.6 and gets lower with the added features, getting to 0.1 (_min_-like) for \(C_{f}=16\). From \(C_{f}=32\) to \(C_{f}=512\), adding new features does not increase the range, and instead reduces it slightly. At \(C_{f}=512\), we can observe that the upper orness limit remains constant, close to 1.0, but the lower limit has gone back to 0.35, losing some _and_-like operators. Recall that in this experiment, the highest \(C_{f}\) were associated with a higher top 5 accuracy.  
Reviewing the dispersion profiles in Figure 4, we can observe how, when the orness profile recedes (\(C_{f}=32\) to \(C_{f}=512\)), the dispersion of the equivalent operators also decreases. Note how the complete dispersion profile curve becomes lower when \(C_{f}\) becomes higher. This means that the operators learned with higher \(C_{f}\) values are more concentrated, with narrower distributions, even for similar orness values. The learned feature of the highest orness (the last feature of each set) can be noted as an example, sharing a similar orness value for each configuration, but with a decreasing dispersion when the number of features is increased.  
These results suggest that learning more OWAs leads the network to explore a certain region of the orness profile meticulously, with many operators that show a low dispersion. In the example configuration, for the total variation metric and \(\alpha=128\), this region lies between orness 0.3 and orness 1.0. Recall that this same region was explored by many more operators when we increased the parameter \(\alpha\) in the first experiment.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(C_{f}\) & **Top 5 acc.** & _p-Value_ \\ \hline Reference & \(52.17\pm 1.5\) & \\
1 & \(52.46\pm 1.4\) & 0.331 \\
2 & \(52.72\pm 1.7\) & 0.176 \\
4 & \(53.38\pm 1.3\) & \(<\)0.001 * \\
8 & \(53.18\pm 1.5\) & 0.007 * \\
16 & \(53.40\pm 1.2\) & \(<\)0.001 * \\
32 & \(53.74\pm 1.7\) & \(<\)0.001 * \\
64 & \(53.88\pm 1.2\) & \(<\)0.001 * \\
128 & \(55.07\pm 1.4\) & \(<\)0.001 * \\
256 & \(55.03\pm 1.2\) & \(<\)0.001 * \\
512 & \(55.35\pm 1.3\) & \(<\)0.001 * \\ \hline \hline \end{tabular}  
* Results marked with
* have better top 5 accuracy than the reference with _p_-value \(<\) 0.05.  
\end{table}
Table 3: Accuracy results by number of learned features.