GNN-LRP

GNN-LRP replaces simple gradient×input attribution with a higher-order Taylor expansion of the model's prediction function at each layer. This captures the joint effect of neuron interactions rather than treating contributions independently. The decomposition distributes relevance proportional to the partial derivatives of the output with respect to the inputs of each layer, ensuring that relevance is conserved across non-linear activation functions like ReLU and tanh.

The core axiom of LRP is the conservation property: the sum of relevance scores at any layer equals the model's output score. In GNN-LRP, this principle is extended to graph convolutions. Relevance is redistributed from a target node's embedding backwards to its neighborhood aggregation step. The method decomposes the message-passing operation (e.g., GraphSAGE or GCN aggregation) by assigning relevance to each incoming message based on its proportional contribution to the node's updated representation.

Unlike node-only explanation methods, GNN-LRP explicitly computes relevance scores for individual edges in the input graph. After backpropagating relevance through the feature transformation and aggregation functions, the method isolates the contribution of each edge's message to the final prediction. This produces a weighted, directed relevance graph where edge weights indicate how critical that connection was for the model's decision, enabling fine-grained structural explanations.

GNN-LRP employs a set of composite propagation rules tailored to different layer types:

• LRP-ε: Adds a small stabilizing term to the denominator to prevent relevance explosion when neuron activations approach zero.
• LRP-γ: Favors positive contributions by adding a multiplicative factor to positive weights, sharpening the explanation's focus on excitatory inputs.
• LRP-αβ: Separates positive and negative weight contributions, weighting them differently to control the influence of inhibitory signals. These rules are applied sequentially through the GNN's layers.

GNN-LRP can generate contrastive explanations that answer 'Why class A instead of class B?' by backpropagating the difference between two output logits rather than a single class score. The relevance signal is initialized as f(x)_A - f(x)_B at the output layer. The resulting node and edge relevance scores highlight the structural patterns that discriminate between the two classes, revealing the specific subgraph features that swayed the model's decision toward one class over the other.

GNN-LRP explanations are evaluated using perturbation-based fidelity metrics:

• Faithfulness: The top-k relevant edges are removed, and the drop in prediction accuracy is measured. A steep drop indicates the explanation captured truly important structures.
• Fidelity: The model's prediction on the subgraph formed by only the top-k relevant edges is compared to its original prediction. High fidelity means the explanation subgraph alone is sufficient to reproduce the decision. GNN-LRP consistently outperforms gradient-based saliency maps on both metrics.

The foundational conservation principle that underpins GNN-LRP. LRP redistributes a model's output prediction backwards through each layer using tailored propagation rules, ensuring that the total relevance is preserved. For graph data, this means relevance flows from the final classification score through message-passing layers back to individual input nodes and edges. The key constraint is that the sum of relevance scores across all input features equals the model's output score, providing a complete decomposition of the prediction.

A mathematical framework for deriving relevance propagation rules used in GNN-LRP. It approximates the model's decision function locally using a first-order Taylor expansion at a root point, then redistributes relevance proportional to the partial derivatives. For GNNs, this yields specific rules for different layer types:

• GCN layers: Use the epsilon-stabilized rule to handle the neighborhood aggregation
• GAT layers: Incorporate attention coefficients into the relevance distribution
• Readout layers: Distribute relevance uniformly or proportionally to node contributions

A downstream application of GNN-LRP relevance scores. After computing node and edge relevance, practitioners can remove low-relevance components to create a sparser, more interpretable subgraph that preserves the original prediction. This process:

• Reduces computational overhead for subsequent analyses
• Identifies the minimal causal subgraph responsible for the prediction
• Enables visualization of only the structurally meaningful graph regions
• Validates explanation quality by measuring prediction fidelity after pruning

The primary quantitative evaluation score for GNN-LRP explanations. Faithfulness measures how accurately the relevance scores reflect the model's true reasoning by removing the most relevant nodes or edges and measuring the drop in prediction performance. A faithful explanation will cause a sharp decline when high-relevance components are deleted. This is typically computed as:

• Area under the perturbation curve: Iteratively removing top-k nodes and tracking accuracy
• Correlation with ground-truth explanations: When synthetic datasets with known motifs are available

A complementary model-agnostic explainer that identifies a compact subgraph and feature subset maximizing mutual information with the GNN's prediction. Unlike GNN-LRP's gradient-based decomposition, GNNExplainer learns a continuous mask over edges and features through optimization. Key differences:

• GNN-LRP: Deterministic, single backward pass, provides fine-grained relevance per node/edge
• GNNExplainer: Requires iterative optimization, produces a binary subgraph selection
• Both methods can be used together for consensus validation of important graph structures

A self-explainable GNN paradigm where a generator module extracts a concise, causal subgraph (the rationale) and a predictor makes decisions based solely on that rationale. GNN-LRP serves as a post-hoc alternative, explaining a pre-trained model without modifying its architecture. The rationalization approach:

• Trains end-to-end with an information bottleneck objective
• Guarantees the explanation is causally sufficient for the prediction
• Contrasts with GNN-LRP's ability to explain any black-box GNN without retraining