Towards a Theoretical Framework for the Explainability of Deep Learning Models

Abstract

Deep learning models have demonstrated outstanding performance in various domains, yet their opaque nature remains a fundamental issue. Explainability aims to bridge this gap by providing insights into model decision-making processes. This paper explores the theoretical foundations of explainability in deep learning, emphasizing mathematical and conceptual perspectives. We investigate the limitations of current approaches and discuss how interdisciplinary methodologies can enhance our understanding of deep learning systems. Additionally, we explore the potential of combining explainability with robustness, fairness, and generalization to create more reliable AI systems. The paper also highlights challenges such as the trade-off between interpretability and predictive power, the scalability of explainability methods, and the lack of standard evaluation metrics. Finally, we propose novel research directions, including topological analysis, causal reasoning, and probabilistic explainability models. A particular focus is placed on the role of human cognition, decision-theoretic frameworks, and explainability as a tool for improving the reliability of deep learning models in high-stakes scenarios. Furthermore, we investigate how explainability techniques can enhance the deployment and optimization of deep learning models in real-world environments, ensuring their ethical and practical applications. This work aims to provide a comprehensive framework for improving the transparency, interpretability, and accountability of AI-driven decision systems.