# Explainable Artificial Intelligence: Advancements and Limitations
## 4 Visual Explanations
### Pixel Attribution
#### 4.2.1 Backpropagation-Based Saliency Mapping  
Backpropagation-based methods are widely used for saliency mapping [60, 63, 73]. In this direction, [PERSON] et al. presented the first saliency mapping technique where they take gradients of a class score \(S_{c}\) for class \(c\) with respect to the pixels of the input image \(\mathbf{x}\)[63]. These gradients result in a relevance score vector, \(\mathbf{r}_{c}=\frac{\partial S_{c}}{\partial\mathbf{x}}\), with the same size as the input image. Higher positive relevance scores indicate important pixels for class \(c\), while lower ones show insignificance. In addition, high negative values can be seen as an indicator of other classes or backgrounds. These relevance scores then can be used to weigh the pixels to create a saliency map [59, 63]. As [PERSON] et al. presented, the other two well-known gradients-based methods, deconvolution [60, 87] and guided backpropagation, indeed follow the same process as [PERSON]'s approach apart from the way they backpropagate through the activation functions [73]. Integrated Gradients [74] provides a principled way to quantify the contribution of each input feature to a model's prediction. It addresses some of the limitations of the early gradient-based methods, which can be noisy or misleading due to local irregularities in the model's gradients. They compute attributions by integrating the gradients of the model's output with respect to the input along a straight path from a baseline (e.g., a black image or zero vector) to the actual input. Mathematically, it averages these gradients over multiple steps along the path, ensuring that the attributions are both robust and meaningful. The author claims that their approach satisfies desirable theoretical properties, such as completeness, which ensures that the sum of all attributions matches the difference between the model output for the input and the baseline. By providing a clear and interpretablemapping of input features to their contributions, Integrated Gradients has been recognised as an important technique in XAI research. Deep learning important features (DeepLIFT) [88] is another backpropagation-based pixel attribution method that provides a robust framework for explaining the predictions of deep networks by comparing the activations of neurons to their reference activations. Unlike gradient-based methods, which can suffer from issues such as vanishing gradients or noise, DeepLIFT assigns contribution scores by tracking the changes in outputs relative to a baseline input. It propagates these contributions backwards through the network using a set of predefined rules to ensure consistency and efficiency. The key innovation of DeepLIFT lies in its ability to handle nonlinearities more effectively by considering both the input and the reference, allowing it to capture meaningful attributions even in complex networks. DeepLIFT is also claimed to satisfy the completeness property (the sum of attributions matches the difference between the model output for the input and the baseline) similar to the Integrated Gradients approach. In addition, it also holds the symmetry (equal changes in symmetric inputs receive equal attributions) property which contributes to their robustness and safe use. LRP (layer-wise relevance propagation) [68; 89; 90; 91] is a powerful explainability technique designed to interpret the decisions of DNNs by tracing back the contributions of individual input features to the model's output. LRP works by decomposing the prediction score and redistributing it layer by layer, from the output back to the input, using a set of conservation rules. This redistribution ensures that the total relevance is preserved at each layer, ultimately assigning relevance scores to input features in a way that reflects their contribution to the prediction. By doing so, LRP is claimed to satisfy important properties such as relevance conservation and provides insights into how specific features, such as pixels in an image, influence the model's output.