where variables  \({ \hat y_i^s}\) and \(r\) denote the ground truth and the malignancy prediction w.r.t. each source sample, respectively.
The ultimate purpose of CMD²A-Net is to accomplish accurate PLDC. To this end, we simultaneously train the coarse segmentation module, domain transfer module, and classifier module. Note that, minimizing segmentation loss alone would cause overfitting to the source domain, and only optimizing domain transfer loss would lead to generalization degradation in the target domain. Therefore, joint optimization on the total loss could facilitate the training process to reach equilibrium, such that the domain-invariant features could be extracted to achieve accurate classification. The total loss \({\mathcal{L}_{Total}}\) can be defined to: