# A Study of OWA Operators Learned in Convolutional Neural Networks
## 7 Conclusions and Future Work  
The OWA layer [13] is a CNN layer capable of augmenting the feature maps in a CNN by aggregating them with OWA operators. This leads to an increase in accuracy for CNNs in image classification problems. In this work, we have explored the OWA layer as a way of combining OWA operators with CNNs, with the objective of studying new ways of learning the weights of OWA operators.  
First we have confirmed the preliminary results reported in [13; 38], observing an improvement in the accuracy of our test network in this specific experimental framework. With respect to our main objective, we have been able to observe how the network generates clean and diverse operators, with orness ranges covering the full spectrum of possibilities. We have also assessed the need for a proper initialization, showing in the first experiment how it can impair the ability of the network to learn diverse operators. The second experiment performed shows how the number of operators learned influences the explored range of possibilities and how the network can extract knowledge even from a small number of operators. Finally, the third experiment has shown how different sorting metrics lead the OWA layer to learn different OWA operators, allowing us to observe how the sorting metric changes the knowledge contributed by the layer.  
The most important results, arguably, come from the final comparison between the learned operators and some theoretical families, namely the Binomial OWA [8], the Stancu OWA [22], and the exponential RIM OWA [23]. Our learned operators are empirically consistent with these parameterizations in most cases, but we have also found several examples of operators that are currently impossible to approximate by these families. Considering the nature of the operators learned by the OWA layer, built from scratch and only driven by the data, we believe that this proves a deficiency in the current models. We hope that these results will aid in the design of new models of OWA operators, less constrained and capable of expressing more complex relationships between the input data.  
Regarding the OWA layer, we hope that future work will unveil new applications where there is a higher margin of improvement, paving the way to new interactions of OWA operators with other AI tools. The results achieved in this work are still constrained to a narrow experimental framework, and should be extended in future works to new datasets and problems to study the differences in the OWAs learned in different applications as well as the usefulness of the OWA layer. In particular, it would be interesting to study the behavior of the modified CNN when applied to larger datasets, such as ImageNet [47] and its version with reduced image resolution, Tiny ImageNet [48].  
Conceptualization, LD.-C., D.P. and M.G.; Data curation, I.D.-C.; Formal analysis, LD.-C.; Funding acquisition, D.P. and M.G.; Investigation, I.D.-C.; Methodology, I.D.-C., D.P. and M.G.; Resources, D.P. and M.G.; Software, I.D.-C.; Supervision, D.P. and M.G.; Validation, D.P. and M.G.; Visualization, I.D.-C.; Writing--original draft, I.D.-C.; Writing--review and editing, I.D.-C., D.P. and M.G. All authors have read and agreed to the published version of the manuscript.  
This work was funded by a predoctoral fellowship of the Research Service of Universidad Publica de Navarra, the Universidad Publica de Navarra under project PJUPNA1926, and the Spanish MICIN (PID2019-108392 GB-I00/ AEI/10.13039/501100011033).  
Data Availability Statement: Data sharing not applicable No new data were created or analyzed in this study. Data sharing is not applicable to this article.