Layer-Wise Relevance Propagation

LRP (Layer-wise Relevance Propagation) is an attribution technique that distributes the model's output prediction backward through the network layers — at each layer, relevance is redistributed to the inputs according to propagation rules, ultimately assigning relevance scores to each input feature.

How LRP Works

• Start: Initialize relevance at the output: $R_j^{(L)} = f(x)$ (the prediction).
• Propagation: Redistribute relevance backward: $R_i^{(l)} = \sum_j \frac{a_i w_{ij}}{\sum_k a_k w_{kj}} R_j^{(l+1)}$.
• Rules: LRP-0 (basic), LRP-$\epsilon$ (numerical stability), LRP-$\gamma$ (favor positive contributions).
• Conservation: Total relevance is conserved at each layer — $\sum_i R_i^{(l)} = \sum_j R_j^{(l+1)}$.

Why It Matters

• Conservation: Relevance is neither created nor destroyed — complete, faithful attribution.
• Layer-Specific Rules: Different propagation rules can be used at different layers for best results.
• Deep Taylor Decomposition: LRP has theoretical connections to Taylor decomposition of the network function.

LRP is backward relevance flow — propagating the prediction backward through the network to trace which inputs were most relevant.