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One Wave To Explain Them All: A Unifying Perspective On Feature Attribution
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Proposes WAM, a feature attribution method that computes gradients with respect to wavelet coefficients (with SmoothGrad and Integrated Gradients variants) to explain classifiers across audio, image, and volume modalities.
Problem
Pixel-based saliency heatmaps fail to capture the structural components of data, and the choice of domain for computing attributions has been overlooked, especially for audio and 3D volumes.
Approach
Compute attributions in the wavelet domain by taking gradients of the classifier with respect to wavelet coefficients of the input, extending SmoothGrad and Integrated Gradients to this domain so the same method applies to any input dimension.
Key results
- On ImageNet with EfficientNet, WAM-IG reaches Insertion 0.447 and Deletion 0.049 (Faithfulness 0.370) versus 0.113/0.113 (Faithfulness 0.000) for Integrated Gradients.
- On AdrenalMNIST3D with 3D Former, WAM-IG achieves Faithfulness 0.098 versus -0.077 for Integrated Gradients and 0.009 for Saliency.
- On ESC-50 audio, WAM-SG attains the best Insertion (0.449) but Integrated Gradients keeps the best Deletion (0.047) and Faithfulness (0.264).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| compute SmoothGrad attributions in the wavelet domain rather than the input domain | SmoothGrad · ESC-50 fold 1 | Insertion: 0.251 -> 0.449 | Helped |
| compute attributions in the wavelet domain rather than the input domain | Integrated Gradients · ESC-50 fold 1 | Faithfulness: 0.264 -> 0.176 | Hurt |
| compute attributions in the wavelet domain rather than the input domain | Integrated Gradients · ImageNet validation | Faithfulness: 0.000 -> 0.370 | Helped |
| compute attributions in the wavelet domain rather than the input domain | Integrated Gradients · AdrenalMNIST3D test | Faithfulness: -0.077 -> 0.098 | Helped |
| compute attributions from the mel spectrogram instead of wavelet coefficients (ablation) | WAM-SG · ESC-50 fold 1 | Insertion: 0.449 -> 0.169 | Hurt |
| compute attributions from the mel spectrogram instead of wavelet coefficients (ablation) | WAM-IG · ESC-50 fold 1 | Insertion: 0.436 -> 0.168 | Hurt |
| replace Haar mother wavelet with Bior or Daubechies (ablation) | WAM-IG · ImageNet and AdrenalMNIST | Insertion: 0.422; 0.404 | No clear effect |
| replace Haar mother wavelet with Bior or Daubechies (ablation) | WAM-IG · ESC-50 | Insertion: 0.438; 0.442; 0.446 | No clear effect |
Surprising findings
- On audio, Integrated Gradients outperforms WAM on Faithfulness and Deletion, so the claim of consistent superiority does not hold across all modalities.
- Explanations computed on mel-spectrograms instead of wavelet coefficients perform much worse on audio faithfulness (near 0).
Limitations
- Does not extend to point cloud data.
- Greedy extraction of important wavelet coefficients is unsuitable for listenable audio explanations.
- Not applicable to text data, limiting use in NLP and multimodal settings.
Experimental setup
Datasets: ESC-50 ImageNet MedMNIST3D AdrenalMNIST3D VesselMNIST SONY-UST
Benchmarks: ESC-50 ImageNet AdrenalMNIST3D SONY-UST
Metrics: Faithfulness Insertion Deletion FF Fid-In mu-Fidelity
Baselines: Integrated Gradients SmoothGrad Saliency GradCAM GradCAM++ Guided Backpropagation
Builds on: Integrated Gradients SmoothGrad Captum LATEC
Closest papers by meaning
- Benchmarking the Attribution Quality of Vision Models (NeurIPS 2024 · similarity 0.88)
- Comprehensive Information Bottleneck for Unveiling Universal Attribution to Interpret Vision Transformers (CVPR 2025 · similarity 0.87)
- How to Probe: Simple Yet Effective Techniques for Improving Post-hoc Explanations (ICLR 2025 · similarity 0.86)
- MFABA: A More Faithful and Accelerated Boundary-Based Attribution Method for Deep Neural Networks (AAAI 2024 · similarity 0.85)
- quanda: An Interpretability Toolkit for Training Data Attribution Evaluation (NeurIPS 2026 · similarity 0.85)
- Less is More: Fewer Interpretable Region via Submodular Subset Selection (ICLR 2024 · similarity 0.85)
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