Deletion Metric

The deletion metric operates by iteratively removing pixels from the input image in descending order of their attributed importance. At each step, the model's prediction probability for the target class is recorded. A sharp, monotonic drop in probability indicates a high-quality attribution map where the method correctly identified the pixels most critical to the model's decision. The area under the resulting probability curve quantifies overall explanation fidelity.

Given an input x, an attribution map A, and a model f, the deletion curve is constructed by:

• Step 1: Rank pixels by descending importance from A.
• Step 2: Sequentially replace the top k pixels with a baseline value (e.g., zero or gray).
• Step 3: Compute f(x_masked) at each step. The Deletion Score is often reported as the Area Over the Curve (AOC) or the drop in log-odds, with lower scores indicating better explanations.

The choice of baseline value for replaced pixels critically impacts the metric. Common strategies include:

• Zero Baseline: Replacing pixels with black (0).
• Blur Baseline: Replacing with a heavily blurred version of the image.
• Noise Baseline: Replacing with random Gaussian noise. A poor baseline can introduce out-of-distribution artifacts that cause spurious probability drops unrelated to feature importance. The blurred baseline is often preferred as it preserves local color statistics while destroying structural information.

The deletion metric serves as a critical sanity check for attribution methods. A truly faithful explanation must outperform random baselines. Key validations include:

• Random Attribution: A random ordering of pixels should produce a significantly slower probability decay.
• Edge Detection: Simple edge detectors (e.g., Sobel) should not outperform sophisticated attribution methods.
• Model Parameter Randomization: If model weights are cascadingly randomized, the deletion curve should degrade, proving the explanation is sensitive to the learned parameters.

The complementary evaluation protocol to the Deletion Metric. Instead of removing pixels, it incrementally adds pixels from most to least important into a blurred or zeroed baseline image. The area under the curve (AUC) of the model's prediction probability as pixels are inserted measures attribution quality. A steep, early rise in probability indicates the attribution map correctly identified the most salient regions. This metric is often paired with deletion to provide a comprehensive view of an explanation's fidelity.

A quantitative evaluation criterion that measures how accurately an attribution map reflects the true importance of features. The core principle is that perturbing the inputs deemed most important by an explanation should cause a correspondingly large change in the model's output. Both the Deletion and Insertion metrics are specific, widely adopted instantiations of the general faithfulness framework. A faithful explanation is one that mirrors the model's actual decision logic, not just plausible-sounding patterns.

An evaluation protocol that goes beyond single-instance perturbation. ROAR iteratively retrains a model from scratch after removing a fraction of the most important features (as ranked by an attribution method) from the entire training dataset. The resulting degradation in the retrained model's performance is measured. If an attribution method identifies truly important features, a model retrained without them should suffer a significant performance drop. This tests whether attributions capture dataset-level signal, not just instance-level noise.

A theoretical framework that defines desirable mathematical properties a feature attribution method must satisfy to be considered reliable. Key axioms include:

• Completeness: Attributions sum to the prediction difference from a baseline.
• Sensitivity: If an input changes and the prediction changes, that input must receive non-zero attribution.
• Implementation Invariance: Two functionally identical models must receive identical attributions. Methods like Integrated Gradients are designed to satisfy these axioms, providing a theoretical guarantee that complements empirical evaluation with the Deletion Metric.

A foundational perturbation-based attribution method that directly inspired the Deletion Metric. It systematically occludes different regions of an input (e.g., with a gray square) and measures the resulting change in the model's prediction probability. The Deletion Metric formalizes this idea into a rigorous evaluation protocol by defining a specific perturbation strategy (progressive removal from most to least important) and a summary statistic (AUC of the probability decay curve).

An optimization-based attribution method that finds the smallest smooth mask that maximally preserves or destroys a model's prediction. Unlike the Deletion Metric, which evaluates a pre-computed attribution map, Extremal Perturbation directly optimizes for a compact, interpretable saliency mask. The resulting masks are naturally smooth and avoid the jittery artifacts common in gradient-based methods. It provides an alternative lens on what constitutes a 'good' explanation: maximal information with minimal input area.