Layer-wise Relevance Propagation (LRP)

The total amount of relevance is preserved as it is propagated backwards from the output layer to the input layer. The sum of the relevance scores assigned to all input features must equal the model's output score for the target class.

• Sum Rule: $\sum_i R_i^{(l)} = f(x)$ for every layer $l$
• Prevents relevance from being artificially created or destroyed during the backward pass
• Ensures the explanation is a true decomposition of the prediction, not just a sensitivity analysis
• Critical for fraud auditing: the exact score that triggered a block is fully accounted for

LRP rules can be designed to propagate only positive relevance, suppressing negative contributions that would otherwise create contradictory, noisy explanations. This is achieved through the $z^+$-rule and LRP-$\alpha_1\beta_0$ propagation.

• Filters out inhibitory or contradictory signals that obscure the primary evidence
• Produces cleaner, sparser heatmaps that highlight only supporting features
• In fraud detection: isolates the transaction attributes that positively contributed to a 'fraudulent' classification
• Contrasts with simple gradient methods that mix positive and negative evidence

LRP can be mathematically derived as a series of Taylor expansions applied at each layer, where the relevance of a neuron is redistributed to its inputs based on their contribution to the neuron's activation. This provides a first-order, local explanation.

• Each redistribution step approximates the function of a single layer
• Provides a theoretical foundation for why LRP works, beyond heuristic rules
• Connects LRP to the broader family of additive feature attribution methods
• Enables the derivation of optimal propagation rules for specific layer types (e.g., ReLU, Tanh)

LRP is not a single algorithm but a framework of composable rules tailored to different layer types. The LRP-$\epsilon$ rule absorbs weak or contradictory relevance, while the LRP-$\gamma$ rule favors positive contributions.

• $z^+$-rule: For ReLU layers, redistributes relevance proportionally to positive weighted activations
• $\epsilon$-rule: Adds a small stabilizing term to the denominator to absorb noise; higher $\epsilon$ produces sparser explanations
• Flat rule: For input layers, distributes relevance uniformly to pixel space
• In fraud models: different rules are applied to dense, convolutional, and embedding layers for optimal clarity

LRP can decompose not just the raw prediction score, but a contrastive quantity: the difference between the score for the predicted class and the score for a competing class. This explains why the model chose class A over class B.

• Decomposes $f_{fraud}(x) - f_{legit}(x)$ instead of just $f_{fraud}(x)$
• Highlights features that are uniquely indicative of fraud versus legitimate transactions
• Eliminates common-mode features that are present in both classes
• Provides a sharper, more actionable signal for fraud investigators reviewing blocked transactions

A single LRP backward pass has a computational cost comparable to a standard forward pass, making it feasible for near-real-time explanation generation in production fraud pipelines.

• Complexity scales linearly with network depth and width
• No sampling, perturbation, or optimization steps required (unlike LIME or SHAP)
• Can be accelerated with batch processing for multiple transactions simultaneously
• Enables inline explanation generation within the real-time fraud scoring pipeline without introducing prohibitive latency

A direct predecessor to LRP that also decomposes a neural network's output prediction by backpropagating contribution scores. DeepLIFT compares the activation of each neuron to a reference activation rather than using a zero baseline, which helps avoid discontinuities in the gradient. This method is crucial for fraud models where a 'neutral' transaction baseline is needed to explain why a specific transaction was flagged as anomalous.

A foundational visualization technique that computes the gradient of the model's output with respect to the input features. While saliency maps highlight which features most influence a classification, they often produce noisy, visually diffuse explanations. LRP improves upon this by applying conservation rules during backpropagation, providing sharper, more robust feature attributions for fraud analysts reviewing high-dimensional transaction vectors.

A model-specific attribution method that computes feature contributions by integrating gradients along a path from a baseline input to the actual input. Unlike LRP's layer-by-layer redistribution, Integrated Gradients satisfies the completeness axiom (output equals sum of attributions). For fraud models, this provides a rigorous mathematical guarantee that the explanation fully accounts for the anomaly score, which is critical for regulatory audit trails.

A game-theoretic framework that unifies several explanation methods, including LRP, under a common mathematical foundation. SHAP values assign each feature an importance score based on its marginal contribution across all possible feature coalitions. While computationally heavier than LRP for deep networks, SHAP provides a model-agnostic standard that compliance teams often prefer for comparing explanations across different fraud detection architectures.

Regulatory-mandated explanations required when a model's output leads to a negative decision, such as blocking a legitimate transaction. While LRP provides a continuous heatmap of feature relevance, reason codes distill this into the top 3-4 human-readable factors. For fraud operations, LRP attributions must be translated into these concise, auditable codes to satisfy regulations like the Fair Credit Reporting Act (FCRA).

A comprehensive, chronological record of all data, model parameters, and logic used for a specific decision. LRP contributes to this trail by providing a deterministic, reproducible decomposition of the model's reasoning for each flagged transaction. This allows auditors to trace exactly which input features—such as transaction amount, location, or device fingerprint—drove the anomaly score, ensuring full traceability for regulatory review.