In fields like autonomous systems, finance, and medical diagnostics, contemporary artificial intelligence (AI) systems, in particular, deep learning models have shown cutting-edge performance. However, because they lack guiding mechanisms for uncertainty quantification, interpretability, and calibration, these models frequently function as opaque black boxes. In order to enable robust, curvature-aware learning through natural gradient descent, this paper suggests a unified statistical framework that integrates Bayesian inference with information geometry. The approach enhances convergence efficiency and epistemic reliability by giving the parameter space a Riemannian structure determined by the Fisher Information Matrix. The suggested model (Bayes + Natural Gradient) performs better than conventional Bayesian models and standard neural networks, according to empirical assessments conducted on synthetic, benchmark, and real-world datasets. The model's accuracy, negative log-likelihood (NLL), and expected calibration error (ECE) on the MNIST subset were 95.0%, 0.109, and 1.9%, respectively, while those of standard SGD-based networks were 92.8%, 0.174, and 6.2%. Themodel demonstrated practical relevance by achieving clinically aligned attention maps, 0.94 AUC, and 85.9% accuracy in a medical imaging case study on diabetic retinopathy detection. This work promotes a mathematically based approach to AI that places an emphasis on transparency, calibration, and decision-making reliability in addition to performance.