Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that highlight regions of the input most relevant to the model's prediction. However, existing methods face a three-way trade-off. Propagation-based approaches are efficient, but they can be biased and architecture-specific. Meanwhile, perturbation-based methods are causally grounded, yet they are expensive and for vision transformers often yield coarse, patch-level explanations. Learning-based explainers are fast but usually optimize surrogate objectives or distill from heuristic teachers. We propose a learning scheme that instead optimizes deletion and insertion metrics directly. Since these metrics depend on non-differentiable sorting and ranking, we frame them as permutation learning and replace the hard sorting with a differentiable relaxation using Gumbel-Sinkhorn. This enables end-to-end training through attribution-guided perturbations of the target model. During inference, our method produces dense, pixel-level attributions in a single forward pass with optional, few-step gradient refinement. Our experiments demonstrate consistent quantitative improvements and sharper, boundary-aligned explanations, particularly for transformer-based vision models.

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