## 5 Discussion  
### Decision Maps for Deep Learning Variations  
Previous evaluations covered the way the three studied decision-map methods--DBM, SDBM, and DeepView--perform over a wide range of classification models. However, in the respective study, we used a single model based on a deep learning architecture (see Section 3.4). It can be argued that with the increasing prominence of deep learning, it is especially important to gather insights into how decision-map methods perform on this particular family of algorithms. We discuss this next by separately studying the decision maps created for four such deep learning architectures. First, we considered the original and relatively simple neural network architecture, already used in previous evaluations, for comparison purposes. This architecture contains three fully connected layers, each with 200 units. Note that, although small, it is an architecture that has been used in previous deep learning applications to compute direct projections [34], inverse projections [25], and decision maps [22]. We then used two larger variants of this architecture, with four layers of 1024 units and four layers of 2048 units, respectively. Finally, we used TabNet [51], a very recent architecture designed for tabular data, which combines the principles of decision trees and neural networks and uses attention mechanisms [52] to prioritize important features during decision making. We did not include more specialized architectures, such as convolutional neural networks (CNN) [53], recurrent neural networks (RNN) [54], long short-term memory (LSTM) networks [55], or deep belief networks (DBMs) [56], in this comparison. Although these architectures are quite powerful, they are usually designed to be used with one particular type of data, e.g., images or time-dependent signals. Figure 11 shows the performance metrics for the three decision-map techniques trained to classify four datasets using the above-mentioned four deep learning architectures. We can see that the four deep learning techniques--that is, within one set of four colored bars in the respective plots--were quite similar. The large differences that occurred were dependent on the dataset or metric, similar to what we saw for the architectures evaluated earlier (see Figure 3). The only outlier in this respect was TabNet when run on the Reuters dataset to compute the SDBM map and, to a much lesser extent, when run on the FashionMNIST dataset to compute the DBM map. We examine these two situations separately below. In the latter case, TabNet achieved low \(ACC_{C}\) but relatively higher \(Cons_{d}\) and \(Cons_{p}\) values. This demonstrates the situation when the classifier \(f\) performs poorly and the decision map is of good quality. This is a very good example of the use of DBMs--the maps can serve as a reliable indicator of the classifier's under-performance. Figure 11: Label-related metrics for different neural networks. NN \(m*n\) denotes a neural network with \(m\) hidden layers, each with \(n\) units. In the former case, TabNet achieved lower scores in all metrics. If we look at the actual decision maps (Figure 12), we can see that these were, for all four architectures, overall quite similar for the same dataset. Moreover, these maps look quite different from those of the other classifiers depicted in Figures 4-6, apart from the neural network classifier for the two sets of images. In other words, the variability of the decision maps was much smaller over one type of architecture (neural networks) than across different architectures, which was expected. However, Figure 12 also shows some subtle differences between the maps in the middle of the depicted data clusters, that is, close to the locations where the decision boundaries appear. This indicates that the four studied deep learning classifiers, indeed, behaved slightly differently in the most uncertain areas. Also, we can see that the more complex the model, the more complex its decision boundaries.