## 2 Proposed Network
### Adversarial-Based Domain Adaptation for Anchor-Free Detector  
In practical applications, we need to apply the trained model (i.e., LogoNet) to a new dataset (target dataset). The model always suffers performance degradation due to domain shift because the distribution of the source dataset (training dataset) is different from that of the target dataset (test dataset). To enhance the generalization of the model, we aim to address model learning towards the distribution of target domain by aligning the output feature maps of source and target domains as close to each other as possible. In order to align the model between two different domains, we exploit the adversarial learning scheme by adding a domain discriminator network in the training phase to detection framework. The architecture of the LogoNet framework with the proposed domain adaptation training scheme is shown in Figure 7, which consists of a feature extraction network and a detection module. The detection module has three heads, heatmaps-head (for generating class-wise heatmaps), offset-head (for identifying object locations), object-size head (for regressing the size of objects). The anchor-free detector generates class-wise heatmaps corresponding to each class using the output feature maps (mid-level output) of the feature extraction network. The offset and size output maps are also generated separately to give complete detection loss. Previously proposed adversarial learning-based schemes [24; 25; 26; 27], which have been introduced primarily for semantic segmentation tasks, make use of the final class-wise output of the feature extraction network. Since anchor-free detectors train the  
Figure 6: (**a**) Convolutional block with our lightweight module (**b**) Convolutional block with CPD method. network to recognize objects in terms of some keypoints, we observed that the use of class-wise heatmaps leads to the loss of some important domain-specific information. It is very important to select the most suitable output feature maps to align the domain gap. In contrast to the previous methods, here we present a domain adaption-based LogoNet network, in which we propose to use the mid-level outputs of feature extraction network. The main advantage of using mid-level output is that it contains essential domain-specific semantic and visual information and is helpful to employ adversarial learning well. Using the design advantages of anchor-free detectors, we assume LogoNet generates mid-level output feature maps for images from the source domain and the target domain. The mid-level output maps of the source images rendered to different detection heads (heatmap-head, offset-head, size-head) to train the network for the respective tasks. Whereas, the mid-level output feature maps of the target images is used to calculate the adversarial loss to match the data distribution of source and target domains. Therefore, we do not need object-level annotations for the target images. We assume that there are \(N\) images with corresponding object-level annotations in the source domain \(S\) with corresponding object-level annotations \(\{x_{i}^{s}\in X_{S},y_{i}^{s}\in Y_{S}\}\) where \(X_{S}\) is a set of input images in the source space, \(Y_{S}\) denotes the set of corresponding labels. Whereas, \(M\) is the number of images in the target domain \(T\) without object-level annotations \(\{x_{i}^{t}\in X_{T}\}\), where \(X_{T}\) denotes the set of images in the target domain. To employ the adversarial learning technique, we add a domain discriminator network with the LogoNet framework that introduces the adversarial loss (\(L_{adv}\)) and classification loss (\(L_{cls}\)). The domain discriminator network consists of 5 convolution layers with a kernel size of 4 \(\times\) 4 and a stride of size 2, each layer is coupled with a leaky-ReLU activation layer with a fixed negative slope of 0.2, except for the last convolution layer. The number of channels is [64; 128; 156; 512; 1] for each layer, respectively. Finally, a classification layer gives classification outputs.