Attribution Prior

Penalizes large differences in feature importance between adjacent inputs, such as neighboring pixels in an image or consecutive time steps in a sequence. This encourages the model to produce spatially or temporally coherent saliency maps.

• Mechanism: Adds a regularization term that minimizes the squared difference or total variation of attributions across neighboring features.
• Use Case: Reducing high-frequency noise in image saliency maps, making them visually interpretable to radiologists.
• Result: Eliminates the 'shattered gradient' problem where explanations appear as white noise.

Forces the model to base its predictions on a small, focused subset of input features rather than distributing importance diffusely. This aligns with the human preference for parsimonious explanations.

• Mechanism: Applies an L1 penalty directly on the computed feature attribution values during training.
• Use Case: In text classification, forcing the model to highlight only the 5-10 most critical words instead of the entire sentence.
• Benefit: Prevents the model from 'hedging' by weakly attending to everything, revealing the true decision boundary.

Encourages the model to select entire predefined groups of features (e.g., a contiguous region of an image or a specific genomic pathway) rather than isolated individual features.

• Mechanism: Uses a group lasso penalty on the attributions, driving the importance of entire feature groups to zero simultaneously.
• Example: In genomics, forcing the model to attribute importance to entire biological pathways rather than scattered single nucleotide polymorphisms (SNPs).
• Advantage: Produces explanations at a semantically meaningful level of abstraction for domain experts.

Penalizes large changes in feature attributions when the input is perturbed by a small, imperceptible amount. This enforces explanation stability.

• Mechanism: Minimizes the Local Lipschitz estimate of the attribution function, ensuring that similar inputs yield similar explanations.
• Use Case: In financial fraud detection, ensuring that a tiny change in a transaction amount doesn't completely flip the feature importance ranking.
• Outcome: Builds trust by guaranteeing that the model's reasoning is not brittle or capricious.

Directly optimizes the infidelity measure during training, ensuring that the attribution scores accurately predict the model's output change when features are perturbed.

• Mechanism: Adds a penalty that minimizes the difference between the actual output change from a perturbation and the dot product of the attribution with the perturbation vector.
• Significance: Moves beyond subjective visual appeal to a mathematically rigorous definition of explanation correctness.
• Result: Guarantees that the highlighted features are causally relevant to the prediction, not just correlated.

Encodes expert knowledge directly into the loss function, such as expecting attributions to be monotonic with a known physical property or symmetric in a specific coordinate system.

• Mechanism: A custom regularization function that penalizes attributions violating known physical laws or logical constraints.
• Example: In computational chemistry, penalizing attributions that don't respect the rotational symmetry of a molecule.
• Power: Transforms the model from a black-box pattern matcher into a physics-compliant reasoning engine.

Penalizes large differences in attribution between adjacent input features, producing spatially coherent saliency maps. This prior is implemented by adding a regularization term that minimizes the squared difference between attributions of neighboring pixels or tokens.

• Use case: Image classification where explanations should have contiguous regions
• Mechanism: Adds a total variation loss on the gradient map during training
• Result: Eliminates the 'salt-and-pepper' noise common in raw gradient saliency maps

Encourages the model to base predictions on a small subset of input features rather than distributing importance diffusely. This is achieved by penalizing the L1 norm of the feature attribution vector during training.

• Use case: Medical diagnosis where clinicians expect decisions based on few biomarkers
• Mechanism: Adds λ||attribution||₁ to the training loss
• Result: Produces concise, human-verifiable explanations with clear feature selection

Directly optimizes for attributions that accurately reflect the model's true decision boundary. The prior minimizes the correlation between the attribution map and random noise, ensuring explanations are not merely plausible but mechanistically accurate.

• Use case: Regulatory compliance where explanations must withstand audit
• Mechanism: Penalizes the model when perturbing highly-attributed features does not change the prediction
• Result: Attributions that causally influence the output rather than correlating incidentally

Enforces that semantically related input features receive similar attribution scores. This is critical when inputs have known groupings, such as pixels belonging to the same object or words in a phrase.

• Use case: NLP models where multi-word expressions should be attributed as a unit
• Mechanism: Penalizes variance in attribution scores within pre-defined feature groups
• Result: Explanations that respect known structural relationships in the input data

Trains the model so that its attributions remain stable under small, adversarially-chosen input perturbations. This prior minimizes the maximum change in the attribution map within an epsilon-ball around each training point.

• Use case: Security-critical applications where explanation manipulation is a threat vector
• Mechanism: Adds a worst-case Lipschitz constraint on the gradient function
• Result: Saliency maps that cannot be radically altered by imperceptible input changes

Encodes domain knowledge that the relationship between certain input features and the output should be strictly monotonic. For example, in credit scoring, higher income should never decrease the approval probability.

• Use case: Regulated financial models requiring logical consistency
• Mechanism: Penalizes negative gradients for features known to have positive monotonic relationships
• Result: Attributions that align with expert domain constraints and regulatory expectations