# On the Reliability Assessment of Artificial Neural Networks Running on AI-Oriented MPSoCs
## 5 Experimental Results
### Ranking of the Criticality of Single Neurons
#### 5.1.3 Final Network-Oriented Score Map  
After the CoA and NoA, a final network-oriented score map was obtained based on the analysis of the class-oriented approach and given the \(t\) parameter. This \(t\) value represents the amount of neurons taken from the classes score maps (always starting from the top positions). By applying (3), i.e., the union (without repetition) operation, we removed duplicate neurons by keeping the highest values assumed among the classes rankings. Therefore, with each \(t\) value, we computed the percentage of neurons with the Equation (3) in the CoA: their value will be compared with that obtained in the initial NoA. Then, for each neuron in the set (3), if its value was higher than that in the NoA, its value was updated in the final score map; otherwise, the highest from the NoA was kept. Next, to study the influence of the CoA on the NoA with a growing \(t\) percentage, we performed a further study on the three CNNs. The first experiment is shown in Figure 6(a) and targets LeNet (MNIST). The x-axis represents the increasing \(t\) percentage, whereas the y-axis shows the corresponding percentage of neurons over the total. The red line outlines the percentage of critical neurons calculated with (3) after the CoA, for the corresponding \(t\) value. The blue line illustrates the percentage of neurons that are updated in the final network-oriented score map due to their higher criticality value. As it turns out, the lower the \(t\) percentage, the higher the percentage of neurons in the set (3), whose value is updated in the final network-oriented score map. For example, when \(t=5\%\) in LeNet (MNIST), the union without repetition (3) includes 6291 critical neurons (red point), meaning the 12% of the total 48,650 neurons. A total of 6212 neurons (blue point) over 6291 (red point) are overwritten with the values obtained from the CoA (3). In other words, 98.74% of neurons has a different level of criticality when moving from the class-oriented to the network-oriented methodology. For higher \(t\) values, this percentage reduces, reaching 45% for \(t=80\%\). Figure 7: Network-oriented analysis with a growing \(t\) percentage of critical neurons from the class-oriented analysis (CoA). A study on the influence of the CoA on the NoA with a growing \(t\) percentage. Furthermore, as illustrated in Figure 7b,c, the same analysis was reproduced for ConvNet (SVHN) and All-CNN (CIFAR-10). Similar to what was discussed for LeNet, the lower the set of critical neurons in (3) (determined by the \(t\) percentage and showed as a red line), the higher the percentage of neurons in this set that will be updated in the final network-oriented score map (blue line). Overall, we can say that even with the highest \(t=80\%\), the number of neurons with a criticality higher in the CoA is approximately half of the total neurons and, as experimentally demonstrated, it depends also on the size of the neural network. Specifically, when \(t=80\%\), we updated 45.57%, 55.64%, 69.04% of neurons (respectively for LeNet, ConvNet, and All-CNN) in the final network-oriented score map. A further observation related also to the size of the targeted neural networks is that the initial set of critical neurons for \(t=5\%\). The smaller the network size, the higher the probability of having replicated neurons. In other words, when \(t=5\%\), the union without repetition yields the following figures: 12.93%, 19.18%, and 35.93% for LeNet, ConvNet, and All-CNN, respectively. Finally, to demonstrate how the proposed profiling methodology behaves with respect to the existing methodology [48] discussed in Section 2.3, we present a further analysis. As stated, the final network-oriented score map contains the network's neurons ordered based on their criticality, reinforced by a \(t\) percentage with the CoA. We carried out software FI campaigns for the three CNNs.