Interpreting Breast Mammograms with Incomplete Lesion Labels Using Logic Tensor Networks

Breast cancer is one of the leading causes of cancer-related mortality worldwide. A large body of research has demonstrated that mammographic screening is effective in reducing both the incidence and mortality of breast cancer. To improve screening efficiency and clinical outcomes, many countries have established systematic breast cancer screening programs to promote early detection and timely intervention. However, many computer-aided detection (CAD) technologies provide only limited improvements in diagnostic accuracy, highlighting shortcomings in feature representation and decision interpretability. Logic Tensor Networks (LTNs), a neurosymbolic framework that combines neural networks with logical reasoning, has shown strong potential in incorporating domain-specific prior knowledge and performing structured prediction tasks. In the context of breast cancer detection, LTNs enable the joint classification of multiple lesion attributes by satisfying logical rules and aggregating intermediate concept labels (e.g., lesion types), thereby enhancing structural consistency and improving model interpretability. Nevertheless, the limited availability of abnormal samples and the substantial cost associated with labeling intermediate concepts in clinical data constrain the practicality of fully supervised LTN models, prompting the exploration of weakly supervised and unsupervised approaches. In response to this challenge, this thesis proposes a weakly supervised LTN training framework that eliminates the need for intermediate concept labels. Instead of relying on fact aggregation, our proposed method introduces four complementary loss functions—structural logical consistency loss (SatAgg loss), entropy regularization, KL divergence, and reconstruction loss—to construct effective structural supervision. The improved approach enables the model to maintain logical coherence and semantic alignment even under weakly supervised conditions. Based on BI-RADS assessment standards and clinical literature, clinically meaningful logical rules were defined as domain-specific prior knowledge. Experimental results demonstrate that the proposed method not only removes the reliance on intermediate concept supervision, but also surpasses the fully supervised approach in both lesion category classification and lesion type prediction. These findings confirm that integrating logic-based structural constraints with multi-loss optimization provides a scalable and interpretable solution, particularly effective in breast cancer screening scenarios with limited annotations.