Thesis title: Interpretability and explainability AI in advanced Neural Networks for Topological Quantum Field Theory and Medical Application
In recent years, Artificial Intelligence has emerged as a fundamental tool in academic research and industrial applications. Despite this rapid development, deep neural networks (DNN) remain black boxes that are difficult to explain and interpret, and this, together with the need for extensive use of training data, represents one of the major limitations in the adoption of these technologies in heterogeneous fields ranging from medical and pharmaceutical applications to fundamental physics and industrial applications.
To date, there is still no unanimous consensus on the meaning of explainability and interpretability associated with DNNs, which is why it is often preferred in the literature to define these concepts on the basis of characteristics that must be fulfilled. However, this practice has other limitations, first of all, it again lacks a unanimous consensus as to what characteristics are needed to make an explanation good, but above all, it lacks a quantitative metric to certify the goodness of the explanation in an objective manner. One of the reasons behind this difficulty in unambiguously defining the concept of explainability lies in the fact that different types of users need different types of explanations, the dominant idea is therefore that no one explanation algorithm alone will be able to satisfy all the characteristics we seek but instead, it will be an explanation ecosystem that answers different types of questions for different users that will satisfy the set goal.
The aim of this doctoral thesis is to study different explainability techniques in two very different contexts, medical imaging and applications in fundamental physics in particular in the context of TQFT. In the first case, we focus on the segmentation of medical images task, where most explainability methods proposed so far provide a visual explanation in terms of an input saliency map. The aim of this work is to extend, implement and test an influence-based explainability algorithm instead, TracIn, proposed originally for classification tasks, in a challenging clinical problem, i.e., multiclass segmentation of tumor brains in multimodal Magnetic Resonance Imaging. We verify the faithfulness of the proposed algorithm linking the similarities of the latent representation of the network to the TracIn output. We further test the capacity of the algorithm to provide local and global explanations, and we suggest that it can be adopted as a tool to select the most relevant features used in the decision process. The method is generalizable for all semantic segmentation tasks where classes are mutually exclusive, which is the standard framework in these cases.
In the second use case, we propose a novel framework for supervised learning based on Topological Quantum Field Theory (TQFT) for understanding the problem of generalisation in Deep Neural Networks. More specifically, in this approach, Deep Neural Networks are viewed as the semi-classical limit of Topological Quantum Neural Network (TQNN). We demonstrated, using the perceptron architecture as a simplified example, that a TQNN can be used to directly compute the parameters needed to generalize from a training set, in the absence of any actual training of the network. This raises the possibility of replacing data-intensive training of DNNs with quantum computations, with a significant increase in efficiency and decrease in operational costs.