Attribution Upsampling should Redistribute, Not Interpolate

State-of-the-art attribution methods such as AttEXplore rely on adversarial sample generation that applies an all-pass filter across the frequency spectrum: they perturb all frequencies of the input image alike, from the low frequencies that carry coarse shape to the high frequencies that carry edges and textures. However, models rely on low and high frequencies to different degrees, and such an all-pass perturbation cannot adapt to the model being explained, which limits the faithfulness of the resulting attribution maps. We propose FAMPE (Frequency-Aware Model Parameter Explorer), an attribution method that overcomes this limitation by perturbing the low- and high-frequency bands of the input independently, so that the perturbation can be shifted toward the band that matters for the model. The boundary between the two bands is set for each image automatically from its spectral energy. On ImageNet with five convolutional neural network and Vision Transformer architectures, FAMPE significantly improves the Insertion Score over the strongest baseline, AttEXplore, on four of them, by up to 15.4%, at essentially the same computational cost. How the perturbed frequency bands are weighted matters: the best and the worst balance between them differ by 19-36% in Insertion Score, and the best balance depends on the architecture. Choosing the balance for each image with a probe that needs no ground truth raises the Insertion Score significantly further on all five architectures, reaching up to 24.4% above AttEXplore. Controlling which frequency band is perturbed is therefore a simple, low-cost way to improve attribution faithfulness.

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. Code and pretrained models are available at https://github.com/dschinagl/AHA.

A central goal of mechanistic interpretability is to identify which internal components causally drive a language model's behavior. Because these importance estimates serve as the evidence for identifying circuits, systematic errors can lead to the misidentification of the underlying mechanisms. While activation patching provides a gold-standard causal metric, its computational cost is prohibitive at scale. Practitioners instead rely on attribution patching, a gradient-based, first-order approximation whose reliability remains poorly understood. In this work, we characterize the source of this unreliability, demonstrating that the dominant error stems from the non-linearities in the downstream network rather than local curvature at the patched component. This insight yields three practical tools: (i) a reliability score to detect untrustworthy estimates, (ii) error bounds quantifying potential attribution mis-specifications, and (iii) a Hessian-vector-product (HVP) correction that eliminates the leading-order error with only one additional backward pass. In evaluations across five model families (124M-9B parameters) and both random-token and naturalistic (name-swap) perturbations, HVP is the only second-order correction feasible at larger scale, where standard baselines like Integrated Gradients become computationally prohibitive. In comparative experiments, a multi-step HVP variant matches or exceeds the accuracy of Integrated Gradients at significantly lower compute, outperforming prior second-order baselines. These improvements lead to higher-fidelity circuit recovery on standard benchmarks and support a Screen-Flag-Fix workflow that targets computational effort only toward the components flagged as unreliable.