# Assessing Efficiency in Artificial Neural Networks
## 4 Results
### Memorization and Generalization  
To test the resistance of networks to overfitting/memorization, a percentage of image labels were randomized before training, as previously described by [PERSON] et al. [6]. Overfitting occurs when incorrect, random labels are learned and is analogous to memorizing the label for an image. Table 3 shows the results for the neural networks with the highest alQ and the highest accuracy from the batch normalization tests for both the LeNet-300-100 and LeNet-5 networks. When none of the labels are randomized (0%), the accuracy of the largest network is higher than the network with the best alQ for both LeNet-300-100 and LeNet-5. When 25-75% of the labels were randomized, the network with the highest alQ had the best accuracy. Even when 75% of the labels were randomly assigned, the networks with a high alQ were able to achieve accuracies of 84.68% and 92.51% for the LeNet-300-100 and LeNet-5 networks, respectively. These numbers are considerably better than the neural networks with the highest accuracies in the batch normalization tests, which had test accuracies of 36.99% and 44.24% when trained on data with 75% of the labels randomized. Both types of networks had poor performance regardless of original alQ or accuracy values when all labels were randomly assigned (100%). This result demonstrates that networks with a high alQ have the property of being resistant to overtraining and memorization and that they can learn the correct classification weights even when a majority of the input labels are incorrect.  
To test the capacity of networks to generalize results to a larger, more diverse dataset, the networks with the highest alQ or the highest accuracy were trained on the MNIST dataset, and classification accuracy was then measured on the EMNIST dataset. The EMNIST digits dataset has a similar format to MNIST, but it contains 280,000 more samples [24]. The general trend was that the network with the highest accuracy showed a superior performance on EMNIST in comparison to MNIST, with significant differences between the LeNet-300-100 and LeNet-5 networks, Table 4). The LeNet-300-100 network with the highest accuracy on MNIST (98.03%) showed a much greater performance than that with the highest accuracy on EMNIST (76.21%), while the network with the highest alQ showed a much larger decrease in accuracy from MNIST to EMNIST (from 93.65% to 58.43%, respectively). In contrast, the differences between the networks with the highest accuracy and the highest alQ were less drastic among the LeNet-5 networks. The EMNIST accuracy was 90.56% in the network with the highest accuracy and was 89.36% in the network with the highest alQ. These experiments were repeated after training the same networks on MNIST with 75% of the labels randomized, and as expected the networks with the highest accuracy showed a significant decrease in performance on EMNIST, while the networks with the highest alQ showed a considerably improved performance on both the LeNet-300-100 and LeNet-5 networks. This data demonstrate that convolutional neural networks with high alQ do not considerably underperform in comparison to much larger networks when performance is assessed on a much larger, diverse dataset, but dense networks with a high alQ may not generalize as well.