## 4 Results and Discussion
### Results
Resnet18 achieved the lowest classification accuracy because of the ReLU activation function. The ReLU function outputs the positive input directly, whereas it outputs zero for negative inputs (x < 0). Therefore, the ReLU activation function fails to activate the neuron when it receives negative inputs, leaving no guarantee that all of the neurons would be active at all times, resulting in the dying ReLU problem. In this case, the network cannot learn using the optimization approach. The dying ReLU problem is undesirable because it causes a large percentage of the network to become idle over time. We can observe in Table 3 that, in the case of different variants of Resnet, accuracy improves with increasing depths of the networks because a deeper DL-based model captures more complicated and essential deep features and increases the network's classification performance. However, as the depth of the network expands, computational complexity increases, which ultimately affects the efficiency of the network. Furthermore, we can conclude from Table 3 that the inceptionresnetv2 TL algorithm is identified as the best classification method for detecting and classifying brain tumors. Figure 4: Training and validation accuracy and loss plots of Inceptionresnetv2 (black line shows the validation accuracy and loss. Also, the blue lines shows training accuracy and red line shows training loss). Inceptionresnetv2 achieved effective results for several reasons. Inceptionresnetv2 achieved the best classification results because of its capability to extract more discriminative, detailed and robust deep features. Inceptionresnetv2 possesses the features of both Resnet and Inception such as wider networks, hyperparameters, kernel filters, etc. The two DL models, i.e., Inception and Resnet, were combined to achieve high-performance results at lower epochs. Each Inception block in Inceptionresnetv2 is followed by \(1\times 1\) convolution without activation, i.e., a filter expansion layer to compensate for the dimensionality reduction caused by the inception block. To better utilize computing resources for the classification experiment, the number of inception blocks was increased by adding BN only on top of traditional layers, not on summations. The benefits of using pre-trained DL frameworks with TL for the detection and classification of brain tumors into meningioma, pituitary and glioma are numerous; for example, the classification method is completely automated, and it removes the traditional stages of noise filtering, ROI delineation, feature extraction and selection. Moreover, the results achieved by the pre-trained DL frameworks are reproducible, and, in contrast to [4; 5; 6; 7], the highest level of accuracy is attained. Furthermore, running pre-trained frameworks with TL on a single CPU computer is computationally expensive. For all pre-trained frameworks, the computation times for the TLs are approximately 159 min, 187 min, 318 min s, 525 min, 667 min, 801 min, 950 min, 1252 min and 1730 min. Even the most efficient model, shufflenet, took 159 min for brain tumor classification. Longer computation times were a result of all models being developed using the MATLAB 2020a platform and running on a PC with an Intel (R) Core (TM) i5-5200U CPU and 8 GB of RAM. The computation times were long because we ran the code in a MATLAB environment with a single CPU.