# Breast Cancer Diagnosis Using YOLO-Based Multiscale Parallel CNN and Flattened Threshold Swish
## 2 Material and Methods
### Proposed Backbone CNN Architecture  
The proposed CNN backbone architecture extracts multiscale features using the Parallel Feature Extraction Stem (PFES), Dense Connection Blocks (DCB), and Inception Blocks (IB), as shown in Figure 3. The PFES extracts multiscale features using four differently sized filters (9 \(\times\) 9, 7 \(\times\) 7, 5 \(\times\) 5, and 3 \(\times\) 3) in its four parallel convolutional layers. These layers extract high-level features in a simple feed-forward manner. In the PFES, after two consecutive convolutional layers, a MaxPooling layer is introduced to downsample the feature maps. The output of the PFES results in 104 \(\times\) 104-dimensional feature maps with 512 channels. Then, a 1 \(\times\) 1 convolution is applied to reduce these feature maps to 256 channels. The 1 \(\times\) 1 convolutional layer is strategically employed as a parameter reduction technique, effectively controlling the overall number of parameters within the network. This approach not only streamlines the model by minimizing computational complexity but also maintains the integrity of feature representation, ensuring efficient processing without compromising performance. MaxPooling layers are used to further reduce the sample dimensions to 52 \(\times\) 52.  
Figure 3: Proposed multiscale parallel CNN architecture.  
After extracting high-level features, these feature maps with dimensions of 52 \(\times\) 52 \(\times\) 256 are fed into the DCB and IB. Four CNN layers use 64 filters of a 3 \(\times\) 3 size each. In the DCB, as the CNN model forward propagates, the relationship between the L-1 th layer and the Lth layer is described in Equation (2).  
\[x^{l}=f\Big{(}x^{l-1}*w^{l}+b^{l}\Big{)} \tag{2}\]  
where f presents the activation function (i.e., FTS), \(x^{l-1}\) is the input, \(w^{j}\) are the kernel weights, \(*\) is the sign for convolution operation, and \(b^{l}\) represents the bias. In the dense connection block, the feature maps of layer L-1 are concatenated and used as the input for the next Lth layer.  
DCB play a vital role in enhancing the model's ability to analyze mammographic images. In DCB, each layer receives inputs from all preceding layers, facilitating the deeper and more efficient propagation of features throughout the network. This design significantly enhances feature reuse and ensures the generation of rich semantic feature maps. These maps are helpful in accommodating the vast irregularities observed in the appearances of breast tissues and the characteristics of lesions in mammograms. Furthermore, the enhanced information flow mitigates the risks of vanishing or exploding gradients, thereby improving the model's training stability and performance across diverse classes.  
IB, inspired by the principles of InceptionNet [37], are integrated into our system to harness their capability of extracting and leveraging features at multiple scales [31]. This block utilizes 1 \(\times\) 1, 3 \(\times\) 3, and 5 \(\times\) 5 convolutional filters for extracting multiscale features. These features are particularly beneficial for addressing the scale variation of lesions, ranging from minute calcifications to larger masses. By capturing patterns at various scales, IB contribute to the model's robustness, enabling it to more effectively identify breast cancer lesions of different sizes and shapes.  
The output feature maps (52 \(\times\) 52 \(\times\) 1024) from the DCB and IB are concatenated. Then, a 1 \(\times\) 1 convolution is applied to reduce these feature maps to 512 channels. MaxPooling layers are used to further reduce the sample dimensions to 26 \(\times\) 26. Subsequently, the resultant feature maps with dimensions of 26 \(\times\) 26 \(\times\) 512 are passed through a second set of DCB and IB. Similar to the previous stages, features are concatenated, reduced in channel count, and dimensionally compressed. These processed features are then fed into the final output layers, which predict all the parameters associated with its GCs, vital for BCD.