A Logic Tensor Network for Breast Cancer Detection in Mammography

The thesis describes an analysis on the application of a novel paradigm in computer vision named Logic Tensor Network (LTN), a branch of Neuro-Symbolic AI, that aims to combine the strengths of symbolic reasoning, provided by First Order Logic (FOL), and Neural Networks (NN). The strategy adopted is based on a patch-level deep learning framework capable of identifying the most common mammographic signs of lesions: microcalcifications and masses, by analyzing patches extracted from the four standard views used in screening mammography: R-CC (Right Craniocaudal), L-CC (Left Craniocaudal), R-MLO (Right Mediolateral Oblique) and L- MLO (Left Mediolateral Oblique). The goal is to predict the status of each individual patch in one of three possible outcomes: Normal - no cancer; Benign - a benign finding; Malignant - dangerous cancer. By combining logical reasoning with neural network learning capabilities, the proposed approach aims not only to improve the accuracy of breast cancer screening, but also to enhance the interpretability, reliability, and generalization of image analysis models. In addition, this research investigates how to incorporate prior domain knowledge into a neural network through the exploitation of LTNs. The framework allows to embed prior knowledge directly into the deep learning architecture in the form of logical rules and facts - we can think of a logical rule as a combination of different facts that has a particular implication. Examples of facts are the concept of "mass" and the concept of a "margin" utilized to describe a mass. A rule can be easily created from these concepts, suppose that a patch contains a "mass" having a "spiculated margin" this is a clear indicator of a suspicious finding (the terms "mass" and "spiculated margin" comes from the Breast Imaging Reporting and Data System, BI-RADS, that is the basis of the prior knowledge used). The effect of these rules and facts will be a regularization effect, that acts directly on the loss. Since some characteristics/patterns are well known in the prior knowledge, the objective is to insert such "concepts" within the architecture of the NN and let the model learns them from data; in fact we will refer to these as trainable predicates. Differently from other frameworks is that we do not specify how a "mass" appears or how a "margin" looks like, all these features will be learnt by the NN - no handcrafted features. In this way, during training the model not only is able to maximize the correctness of a prediction, but is also constrained to satisfy all the predicates that are given as knowledge base. In conclusion, to assess the quality of the LTN a comparison has been made with a Baseline model trained using Focal loss. Results show that the models trained with neurosymbolic approach outperform the Baseline in terms of AUC (area under the ROC curve). For the LTN framework also other metrics have been considerd F-Score, Precision, Recall, Accuracy. These metrics have been used to assess the capacity of the model to recognize lesion within a patch, this is in line with the principle of increasing the explainability.