Faithfulness Metrics

A faithful explanation must account for the total model output. Completeness ensures that the sum of all feature attributions equals the difference between the model's prediction and a baseline. If an explanation leaves residual, unaccounted influence, it is not fully faithful.

• Additivity: Attribution scores sum to the exact output value
• Baseline reference: Typically a zero-information or neutral input
• Violation example: An explanation highlighting only 3 of 5 critical biomarkers, leaving 40% of the prediction unexplained

A faithfulness metric must respond exclusively to changes in the model's function, not to irrelevant input perturbations. If a feature is altered and the model's output changes, the explanation must reflect that change. Conversely, if the model is invariant to a feature, the attribution must be zero.

• Sensitivity-n: For any input differing in one feature, if outputs differ, that feature must receive non-zero attribution
• Implementation invariance: Two functionally identical networks must yield identical explanations
• Diagnostic relevance: Ensures the metric captures true model reliance on biomarkers, not spurious correlations

Two models that compute identical mathematical functions must receive identical explanations, regardless of their internal architecture. A faithfulness metric that produces different attributions for functionally equivalent networks is measuring implementation artifacts, not true model reasoning.

• Functional equivalence: Networks with different weights but identical input-output mappings
• Architecture agnostic: Applies whether the model is a transformer, CNN, or ensemble
• Regulatory implication: FDA reviewers can trust explanations independent of model architecture choices

Faithfulness metrics should preserve linear composition. If a model is a linear combination of sub-models, the explanation of the composite must equal the same linear combination of individual explanations. This property ensures consistency across ensemble methods and multi-task diagnostic models.

• Ensemble consistency: Explanation of a weighted average equals the weighted average of explanations
• Multi-task support: Enables decomposition of explanations for models predicting multiple clinical endpoints
• Practical use: Validates that biomarker attributions remain coherent when combining specialist models

If two features play identical roles in the model's computation, they must receive identical attribution scores. A faithfulness metric that assigns different importance to symmetric features is introducing bias unrelated to the model's true reasoning process.

• Feature interchangeability: Two biomarkers with identical statistical relationships to the output
• Invariance to labeling: Renaming symmetric features must not change their relative attributions
• Clinical example: Two correlated inflammatory markers with equal predictive power must receive equal importance scores

A feature that contributes zero influence to the model's output must receive exactly zero attribution. This property prevents explanation methods from distributing importance to irrelevant inputs, which would mislead clinicians about which biomarkers actually drive a diagnosis.

• Zero contribution: A feature the model completely ignores
• Dummy feature test: Inserting a random noise variable should yield zero attribution
• Regulatory value: Demonstrates the explanation method does not hallucinate importance for non-predictive biomarkers