Insertion Metric

The metric operates by starting with a baseline input, typically a heavily blurred or zeroed-out image. Pixels are then incrementally added in order of their attributed importance—from the most important to the least important. At each step, the model's softmax probability for the target class is recorded. A high-quality attribution map will cause the probability curve to rise steeply, indicating that the most salient pixels were correctly identified and inserted first.

The final score is typically calculated as the Area Under the Insertion Curve (AUC). This summarizes the entire insertion trajectory into a single scalar value.

• Higher AUC: Indicates a superior attribution map that correctly ranks salient pixels, leading to rapid probability recovery.
• Lower AUC: Suggests the attribution method failed to distinguish critical features from noise. The AUC provides a direct, comparative benchmark for evaluating different attribution algorithms on the same model and input.

The Insertion Metric is the direct counterpart to the Deletion Metric. While deletion measures the drop in probability as important pixels are removed, insertion measures the recovery as they are added back. Together, they form a comprehensive evaluation framework:

• Deletion Curve: Should show a sharp decline.
• Insertion Curve: Should show a sharp incline. A faithful explanation will simultaneously score well on both metrics, proving it has correctly isolated the information necessary for the prediction.

The choice of the baseline input is a critical hyperparameter. Common baselines include:

• Gaussian Blur: Replaces pixel information with local averages, destroying high-frequency details.
• Constant Value: Sets all pixels to zero (black) or a mean channel value.
• Noise: Fills the image with random Gaussian noise. The baseline must represent a true absence of information. An unrepresentative baseline can artificially inflate or deflate the metric, making it essential to document the baseline strategy when reporting scores.

Beyond the final AUC, the shape of the insertion curve itself provides diagnostic information. A logarithmic curve that rises instantly suggests the attribution map is highly concentrated on a few critical pixels. A linear curve indicates a more diffuse attribution. Analyzing the curve's gradient at different fractions of inserted pixels helps engineers understand the sparsity and precision of the explanation, revealing whether the model relies on a small, interpretable region or a broad texture pattern.

The metric can be applied to different output layers of the model. While softmax probability is standard for classification, evaluating the logit score (pre-softmax) can be more sensitive to changes in model confidence. Using logits avoids the saturation effect of the softmax function, where probability approaches 1.0 and stops changing. For fine-grained comparisons between attribution methods, monitoring the raw logit insertion curve often reveals distinctions that are compressed in probability space.