Axiomatic Attribution

The principle that the sum of all feature attributions must equal the difference between the model's output for the target input and a baseline reference. This ensures a conservation of relevance—no importance is created or destroyed during the decomposition. Integrated Gradients and DeepLIFT are explicitly designed to satisfy this axiom, making them suitable for high-stakes auditing where total accountability is required.

This axiom demands that two functionally identical networks produce identical attributions, regardless of their internal architecture. If Model A and Model B always output the same value for every input, their explanations must match. This is a critical test for path methods like Integrated Gradients, which depend only on the function's input-output behavior, not the specific weights or layers used to achieve it.

A strict requirement: if a model's output is mathematically independent of a specific feature, that feature must receive an attribution of exactly zero. This prevents irrelevant features from being assigned spurious importance. Gradient × Input methods can violate this axiom when the gradient is zero but the input value is non-zero, highlighting a key failure mode in simple saliency approaches.

A canonical path method that satisfies Completeness, Sensitivity-n, and Implementation Invariance. It computes importance by accumulating gradients along a straight-line path from a baseline (e.g., a black image) to the actual input. The integral captures how each feature incrementally contributes to the prediction change, providing a theoretically sound and widely adopted attribution baseline.

An approximation of Shapley values that leverages the expected gradients of a model with respect to a background distribution. By adding Gaussian noise to inputs for computational efficiency, it bridges game theory and gradient-based sensitivity. This method inherits the strong theoretical guarantees of SHAP while scaling to deep networks, though it sacrifices strict axiomatic purity for speed.

A quantitative metric for evaluating attribution faithfulness. It measures the error between the actual model output change and the dot product of the attribution vector with a meaningful perturbation. A low infidelity score indicates the explanation accurately predicts the model's local behavior. This provides a practical tool for benchmarking methods like FullGrad against the theoretical ideals of axiomatic attribution.