# Enhancing Neural Network Interpretability Through Deep Prior-Guided Expected Gradients
## 1 Introduction
In practice, selecting an appropriate baseline in integrated gradients can be challenging. For example, in medical datasets, setting a blood glucose value of zero to represent missingness is inappropriate, as low blood glucose itself may indicate a hazardous condition. Similarly, in image data, a zero baseline can lead to \"blindness\" in scenarios where pixels identical to the baseline color (e.g., black pixels) fail to be distinguished. Expected gradients mitigate this issue by sampling multiple baselines from a distribution and averaging them, resulting in smoother and more robust explanations. Nevertheless, questions remain about whether the average of these baselines truly represents feature missingness. To address these challenges, we propose incorporating prior knowledge into baselines to better align them with the concept of missingness. Prior information is widely used in traditional tasks such as image segmentation, where it often includes appearance priors and shape priors. For instance, appearance priors leverage distributions of intensity, color, or texture characteristics in target objects to construct segmentation models that match expected appearances, often modeled using multivariate Gaussian models. Conversely, shape priors utilize typical geometric shapes of objects, such as organ structures, to guide segmentation boundaries [26]. While priors are extensively applied in computer vision, their integration into interpretability methods remains limited. Existing methods that incorporate priors, such as BayLIME [27], introduce prior knowledge during linear model training, which is unsuitable for addressing baseline alignment issues in gradient-based attribution methods. This study introduces a framework for expected gradient explanations that incorporates a novel prior-based baseline. The core concept of expected gradients is to quantify the contribution of each input feature to the final decision by integrating gradients along the path from the baseline \(x^{\prime}\) to the input image \(x\), and then taking the expectation. However, traditional baselines in expected gradients often fail to effectively align with the concept of missingness, potentially introducing interpretive bias. To address this limitation, we propose using a prior baseline defined as \(x^{\prime}_{\text{prior}}=x^{\prime}-p_{\text{prior}}\), which incorporates prior information to enable a more precise representation of \"missing\". Unlike conventional baselines, which serve as simple statistical measures of the original data, our prior baseline acts as a flexible reference point that emphasizes prior information, enhancing interpretive fidelity by accurately reflecting feature absence. By subtracting a probability distribution, we create a neutral and objective reference that strengthens the capacity of expected gradients to reveal feature contributions, particularly those distinguishing objects from their background. The primary contributions of this paper are as follows. * A deep prior-guided EG framework, DeepPrior-EG, is proposed to address the long-standing misalignment between baselines and the concept of missingness. It initiates gradient path integration from learned prior baselines, computing expected gradients along the trajectory to the input image. These priors are extracted from intrinsic deep features of CNN layers. * Two prior modeling strategies are developed within the framework: a multivariate Gaussian model (MGM) capturing high-dimensional feature interdependencies, and a Bayesian nonparametric Gaussian mixture model (BGMM) that adaptively infers mixture complexity to represent heterogeneous feature distributions. * An explanation-driven retraining paradigm is implemented, wherein the model is fine-tuned using insights derived from the framework. This enhances robustness and reduces interference from irrelevant background features. * DeepPrior-EG is thoroughly evaluated using diverse qualitative and quantitative interpretability metrics.