Toward Clinically Trustworthy Deep Learning in Cardiology: A Unified Mathematical Synthesis of Representation, Optimization, and Reliability

Background: Deep learning (DL) has revolutionized cardiovascular medicine by allowing for automated analysis of electrocardiography, imaging of the heart, and multimodal clinical datasets. Although there have been impressive advancements in terms of predictive performance, the deployment of DL methods in a clinical setting remains limited due to lack of sufficient mathematical understanding around the concepts of uncertainty, robustness, fairness, explainability, and generalizability. Methods: In this work, a systematic review is conducted using PRISMA principles on 79 peer-reviewed articles published from 2017 until 2025, with a unifying mathematical perspective on the notion of trustworthy deep learning in cardiology. Results: We find that there is significant discrepancy between prediction accuracy and clinical reliability, with little emphasis placed on mathematical guarantees, reproducibility of evaluation procedures, calibration, or robustness verification. To address this challenge, we propose a conceptual mathematical framework which brings together the elements of representation learning, optimization, and trustworthiness into a unified audit of AI in cardiac care. We note that the presented indices are purely theoretical and are meant to provide guidance for future standardization, and as such do not represent actual clinical metrics. Conclusions: Although our paper does not propose any new predictive algorithms, we do contribute a strong theoretical basis for the evaluation and development of clinically reliable deep learning algorithms in cardiology.