Mathematical Framework for Explainable Vehicle Systems Integrating Graph-Theoretic Road Geometry and Constrained Optimization

Abstract

Deep learning models are widely used in autonomous vehicle systems for perception, localization, and decision-making. However, their lack of transparency poses significant challenges in safety-critical environments. This systematic review presents a unified mathematical framework for explainable deep learning which integrates multimodal inputs, graph-theoretic road geometry, uncertainty modeling, and intrinsically interpretable representations. Road-structured priors that include lane topology and spatial constraints are incorporated into learning and optimization processes for ensuring model predictions and explanations to remain physically and semantically grounded. The review synthesizes methods across saliency-based, concept-based, causal, and intrinsic explainability, and extends them to vision-language models. This enables language-grounded, human-interpretable reasoning in autonomous vehicle systems. While vision-language models offer a new paradigm for semantic explainability, their limitations such as hallucinations, misgrounding, and reduced reliability under distribution shifts are also critically examined. Along with the role of road priors in improving alignment and robustness, another key contribution of this work is its quantitative evaluation metrics for road-aware explainability. These evaluation metrics link the explanations to spatial consistency, uncertainty alignment, and graph-structured reasoning. The overall framework connects latent representations, predictions, and explanations within a single formulation, enabling systematic comparison and analysis across models. Based on a PRISMA-guided review of 164 studies, this research identifies gaps in real-world reliability, temporal reasoning, and standardized evaluation, and outlines future directions including human-in-the-loop systems, regulatory readiness, and language-based auditing. Overall, this study advances a mathematically grounded and road-aware perspective on explainable vehicle AI which significantly bridges the gap between high-performance models and transparent, trustworthy autonomous systems.