AOPC

AOPC operates by iteratively masking the most salient nucleotides identified by an attribution map and recording the model's prediction probability at each step. The process involves:

• Ranking all input positions by their attribution scores (highest to lowest)
• Perturbing the top-k most salient features (e.g., replacing them with a baseline token or reference allele)
• Recording the drop in the target class probability after each perturbation
• Plotting the probability curve as a function of the fraction of perturbed features The area over this curve represents the total explanatory power of the attribution method.

AOPC can be computed under two complementary perturbation orders that test different aspects of attribution quality:

• MoRF (Most Relevant First): Removes features in descending order of attribution. A steep drop in probability indicates the method correctly identified the most critical nucleotides. This is the standard AOPC calculation.
• LeRF (Least Relevant First): Removes features in ascending order of attribution. The probability should remain stable until the least relevant features are exhausted, confirming that low-attribution regions are truly non-essential. A high-quality attribution map exhibits a large AOPC under MoRF and a small AOPC under LeRF, demonstrating both sensitivity and specificity.

Formally, AOPC is defined as the area over the perturbation curve for the top-L most relevant features:

AOPC(L) = (1/L) * Σ_{k=1}^{L} [f(x) - f(x_{MoRF}^{(k)})]

Where:

• f(x) is the model's prediction probability for the original input sequence
• x_{MoRF}^{(k)} is the input with the top-k most relevant features perturbed
• L is the total number of perturbation steps evaluated

A higher AOPC value indicates a more faithful attribution map, as removing the identified features causes a larger cumulative drop in prediction confidence. The metric is often normalized by the total number of features to enable comparison across sequences of different lengths.

The choice of perturbation baseline critically impacts AOPC evaluation in genomic models:

• Zeroing/Mean Imputation: Replacing nucleotides with a zero embedding vector or the mean activation. Simple but may create out-of-distribution inputs that artificially degrade performance.
• Reference Nucleotide Substitution: Replacing the salient base with a fixed reference (e.g., 'A' or 'N'). Common in variant effect prediction contexts.
• Dinucleotide Shuffling: Preserving local nucleotide composition while destroying motif syntax. More conservative and maintains sequence statistics.
• Gaussian Noise Injection: Adding calibrated noise to the embedding at salient positions. Tests robustness without creating artificial sequence artifacts. The selected strategy must balance biological plausibility with the need to isolate the contribution of specific features.

AOPC belongs to a family of perturbation-based faithfulness metrics that evaluate attribution maps through causal intervention:

• AOPC measures the area over the probability curve, providing a summary statistic of degradation across all perturbation steps.
• Log-odds Score: Evaluates the average log-odds difference between original and perturbed predictions, often used as a variant of AOPC.
• ROAR (RemOve And Retrain): Extends AOPC by retraining the model after feature removal, testing whether the attributions identify features the model genuinely relies on rather than spurious correlations.
• Infidelity Measure: Quantifies the expected error between the perturbation in input space and the corresponding perturbation in the attribution map itself. AOPC is often preferred for its intuitive interpretation and direct connection to the model's decision boundary.

Despite its widespread use, AOPC has known limitations that must be addressed through rigorous sanity checks:

• Out-of-Distribution (OOD) Artifacts: Perturbed sequences may fall outside the training distribution, causing prediction drops unrelated to feature importance. Mitigation: Use conservative baselines like dinucleotide shuffling.
• Correlated Feature Masking: In genomic sequences, adjacent nucleotides often contribute jointly to motif recognition. Removing one may not degrade performance if its neighbor compensates.
• Model Parameter Randomization Test: A critical sanity check where model weights are progressively randomized. A valid attribution method should produce different (degraded) AOPC scores on randomized models.
• Data Randomization Test: Training on permuted labels should yield attributions with poor AOPC, confirming the metric captures learned rather than arbitrary patterns.

AOPC belongs to the class of faithfulness metrics, which evaluate how accurately an attribution map reflects the model's true decision logic. These metrics rely on input perturbation—if removing the 'most important' nucleotides causes a steep drop in confidence, the map is considered faithful.

• AOPC: Sequential removal of top-k salient features
• LOg-odds Score: Measures probability shift between reference and alternate alleles
• Keep and Remove Retraining (ROAR): Retrains the model after feature removal to prevent distribution shift

The infidelity measure quantifies the expected error between a significant perturbation to the input sequence and the corresponding perturbation predicted by the attribution map. It provides a complementary perspective to AOPC.

• Defined as the difference between the model's output change and the dot product of the attribution map with the perturbation vector
• A lower infidelity score indicates a more locally accurate explanation
• Often used alongside sensitivity analysis to provide a complete picture of explanation quality

ROAR is a benchmarking framework that addresses a key limitation of AOPC: the out-of-distribution nature of perturbed sequences. Instead of simply masking nucleotides, ROAR iteratively retrains the genomic model after removing the most relevant features.

• If the attribution method is faithful, retrained model performance should degrade rapidly
• Prevents the model from relying on spurious correlations after feature removal
• Considered a gold-standard evaluation for nucleotide-level attribution methods

Attribution sanity checks are a suite of tests designed to verify that an interpretability method is genuinely sensitive to the learned parameters of the genomic model, not just the input data.

• Model Parameter Randomization Test: Randomizing the model's weights should produce different attributions; if not, the method is flawed
• Data Randomization Test: Training on permuted labels should yield different explanations
• These checks ensure that AOPC evaluations are measuring real model behavior, not artifacts

Delta scores represent the quantitative difference in a model's prediction score between a reference allele and an alternate allele. This is the foundational signal that AOPC and related metrics seek to decompose and explain.

• Used extensively in variant effect prediction to assess functional impact
• A large negative delta score indicates a potentially deleterious mutation
• Attribution maps reveal which nucleotides drive the delta score, enabling mechanistic interpretation

In-silico Mutagenesis (ISM) is a systematic perturbation technique that computationally mutates every nucleotide in a sequence to all possible alternate bases, quantifying the impact on model predictions. It is a direct, exhaustive alternative to AOPC.

• Produces a mutation effect map for every position
• Computationally expensive for long sequences (4 x L predictions)
• AOPC can be seen as a targeted, efficient approximation that focuses only on the most salient positions identified by an attribution map