# Towards Explainable Quantum Machine Learning for Mobile Malware Detection and Classification +
## 3 Method
### Model Research and Implementation  
This step is aimed at defining the convolutional and quantum models for the design's comparison. In particular, we considered the following deep learning models: _AlexNet_, a Convolutional Neural Network developed by the authors in [17] (i.e., Standard-CNN), _VGG16_, a Hybrid Quantum Convolutional Neural Network (i.e., CNN with a layer that uses transformations in circuits to simulate a quantum convolution), and a Quantum Neural Network (i.e., a fully quantum model considering two-qubit gates, with the readout qubit always acted upon). In the following, we introduce in detail the considered (convolutional and quantum) deep learning models:  
* **Standard-CNN:** From 2012, CNNs conquered a plethora of of the ICISSP, 22 gen-24 gen 2018 2018 tasks and are currently growing at a rapid pace. There are differences in their architecture, but all the CNN models are based on the principle of the convolutional filter. This filter, called the _kernel_, is applied to the pixel matrix that composes the image on the three RGB levels. We report the structure of the CNN proposed by the authors in [17] in Listing 1. The idea is to consider a lighter model if compared to state-of-the-art models (as, for instance, **VGG16** also exploited in the comparison). For the **Standard-CNN**, the following layers (usually considered by typical CNN models) are exploited: _convolutional_, _Maxpooling_, _Dropout_, and _Dense_ layers;
* **Visual Geometry Group 16**: This network, also known as VGG-16 [33], was designed and developed in 2014 to solve difficult image classification tasks by exploiting ImageNet, an extended dataset composed of 1000 different output labels belonging to  
Figure 4: The workflow of the proposed method: starting from a dataset of Android applications, converted to grayscale images, a set of convolutional and quantum models is considered to build classifiers aimed to discriminate between malware and Trusted applications, by considering Grad-CAM to provide explainability in terms of graphical information about the area of the images that influenced the prediction. different domains. The VGG16 network demonstrated that network depth is a crucial factor to increase classification accuracy in deep learning. The VGG16 model is composed of several convolution layers, each one with a 3 \(\times\) 3 filter and Maxpooling layers considering a 2 \(\times\) 2 filter. The 16 in VGG16 is related to the 16 layers with trainable weights in its architecture. The last model part is composed of 2 fully connected (_Dense_) layers with a softmax activation to perform the classification task. One of the most typical approaches for VGG16's training is devoted to keeping the convolutional part of the model with the weights obtained from training the model on the ImageNet dataset, while the Dense layers part is trained for the specific classification task required;
* **Visual Geometry Group 19:** Also known as VGG19, it was introduced by Oxford University following VGG16 [33]. This network differs from the previous because it exploits 19 layers: sixteen convolutional layers and three fully connected ones;
* **MobileNet:** was introduced in 2017 by Google [35]. This model is based on depthwise separable convolutions, with a single filter applied to each input channel. Different from the standard convolution, MobileNet splits the inputs into two layers, where one layer filters and separates (called depthwise convolutions) and the other combines (called pointwise convolutions). Deeper, the latter layer, allows the creation of a linear combination of the output of the depthwise layer. This strategy significantly reduces the computation and model size. MobileNet can be used in different fields, such as object detection, fine-grained classification, face attributes, and landmark recognition, where the model can obtain good results;
* **EfficientNet:** This was presented in 2019 [36] and is based on the MobileNet-V2 scale-up models in a simple, but effective way using a technique known as the compound coefficient.