Saliency Maps on Graphs

The core mechanism computes the partial derivative of the target class score with respect to the input features or adjacency matrix. Nodes or edges with larger absolute gradient magnitudes are deemed more salient. This provides a direct, first-order approximation of local sensitivity.

• Vanilla Gradient: Computes raw input gradients, often noisy.
• Gradient × Input: Multiplies the gradient by the input value to sharpen the attribution signal.
• Integrated Gradients: Accumulates gradients along a path from a neutral baseline graph to the actual input, satisfying the completeness axiom.

Saliency maps can be computed at two distinct levels of granularity, depending on the analytical goal.

• Node Saliency: The importance of a node v is derived from the gradient of the prediction with respect to its feature vector x_v. This highlights influential entities.
• Edge Saliency: The importance of an edge (u, v) is derived from the gradient with respect to the adjacency matrix entry A_{uv}. This identifies critical relational pathways.

A common technique is to compute edge saliency as the absolute gradient of the loss with respect to the edge weight.

Raw gradient saliency maps on discrete graph structures are often visually noisy and difficult to interpret. SmoothGrad addresses this by injecting Gaussian noise into the input features multiple times and averaging the resulting saliency maps.

• Process: Add random noise to node features N times, compute the saliency map for each noisy input, and average them.
• Result: The averaging process cancels out high-frequency noise while preserving the true structural signal.
• Benefit: Produces a sharper, more coherent visualization of the subgraph driving the prediction.

A modified backpropagation technique that restricts the flow of gradients to only positive signals, effectively suppressing negative contributions that might cancel out positive ones. When applied to GNNs, it sharpens the saliency map by focusing solely on excitatory structural pathways.

• Standard Backprop: Allows both positive and negative gradients to flow.
• Guided Backprop: Applies a ReLU operation to the gradients during the backward pass, zeroing out negative values.
• Effect on Graphs: Highlights only the nodes and edges that positively contribute to the predicted class, providing a cleaner explanatory subgraph.

Adapts the CAM principle to graph domains by projecting the weights of the final global pooling layer back onto the node feature maps. This requires a specific architecture where a global average pooling layer directly precedes the final classification layer.

• Mechanism: The class score is a weighted sum of the pooled node features. The weights define the importance of each feature channel.
• Graph-CAM: Combines these channel weights with the spatial node feature maps to generate a node-level saliency map.
• Limitation: Restricted to GNN architectures ending with global average pooling, making it less flexible than gradient-based methods.

Instead of computing the gradient of the predicted class score, contrastive methods compute the gradient of the difference between the predicted class score and a counterfactual class score. This directly answers the question: 'Why did the model predict class A instead of class B?'

• Contrastive Gradient: ∇_x (f(x)_predicted - f(x)_counterfactual).
• Advantage: Isolates the structural features that are uniquely discriminative for the predicted class relative to a specific alternative.
• Use Case: Highly effective for molecular property prediction where distinguishing between similar functional groups is critical.