# Enhancing Neural Network Interpretability Through Deep Prior-Guided Expected Gradients
## 1 Introduction  
The rapid advancement of Artificial Intelligence (AI) technologies has profoundly transformed a wide range of fields, including natural sciences, medicine, and engineering [1, 2, 3]. In these domains, AI has not only improved the efficiency of data analysis but also optimized experimental processes and design workflows. However, as deep neural networks (DNNs) achieve remarkable success in areas such as computer vision, their \"black-box\" nature has become increasingly apparent. This lack of transparency in decision-making processes raises significant concerns about trust and safety in criticalapplications such as medical diagnostics, financial decision-making, and autonomous driving [4]. Consequently, enhancing model interpretability has emerged as a crucial research objective [5; 6]. Explainable AI (XAI) addresses this challenge by developing models that provide not only accurate predictions but also transparent explanations of their decision-making processes, thereby improving reliability and enabling users to better understand their internal mechanisms [7]. XAI methods are generally categorized into two main types: intrinsically interpretable models and post hoc explanation techniques [8; 9]. Intrinsically interpretable models, such as decision trees, linear regression, and logistic regression, generate predictions based on clear rules or linear relationships, making them inherently traceable and interpretable [10; 11; 12], while recent advances in metaheuristic optimization (e.g., animal migration algorithms for extreme learning machine tuning [13] and modified whale optimization for forecasting models [14] have enhanced the performance of simple architectures, these approaches primarily address computational efficiency rather than interpretability. However, these models are often limited in their ability to handle high-dimensional data and complex nonlinear relationships [15; 16; 17]. As a result, for complex models like DNNs, post hoc explanation methods have become the dominant approach. Among post hoc explanation methods, feature attribution techniques have emerged as essential tools for interpreting the behavior of DNNs [18]. These methods aim to reveal the influence of input features on model predictions, providing insights into how decisions are made. For example, interpretable deep learning models have been shown to assist medical professionals in understanding prediction rationales, ultimately improving decision-making in clinical settings [19; 20; 21; 22]. Gradient-based attribution methods are among the most widely used approaches in feature attribution. Integrated gradients, a prominent technique within this category, quantify the contribution of each input feature by integrating gradients along the path from a baseline to the input [23]. This method addresses key limitations of earlier gradient-based approaches, particularly regarding sensitivity and implementation invariance. For instance, the sensitivity axiom ensures that a feature's significant influence is reflected in the attribution results, while implementation invariance guarantees consistent attributions for functionally equivalent neural networks [24]. In contrast, methods like DeepLIFT [20] and layer-wise relevance propagation [21], which rely on discrete gradients, fail to satisfy these axioms. Expected gradients extend integrated gradients by using the dataset expectation as a baseline, reducing dependency on a single baseline and addressing the \"blindness\" issue inherent in integrated gradients [25]. This approach provides smoother interpretations and greater robustness to noise. In both integrated gradients and expected gradients, the baseline plays a critical role as a hyperparameter, representing the starting point for simulating feature \"missingness\" [19]. From a game-theoretic perspective, the contribution of participants is measured by incremental changes, analogous to evaluating feature importance by assessing the impact of transitioning from \"missing\" to \"present\" on model output.