Extremal Contours: Gradient-driven contours for compact visual attribution

Reza Karimzadeh, Albert Alonso, Frans Zdyb, Julius B. Kirkegaard, Bulat Ibragimov
Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), PMLR 307:201-210, 2026.

Abstract

Faithful yet compact explanations for vision models remain a challenge, as commonly used dense perturbation masks are often fragmented and overfitted, needing careful post-processing. Here, we present a training-free explanation method that replaces dense masks with smooth tunable contours. A star-convex region is parameterized by a truncated Fourier series and optimized under an extremal preserve/delete objective using the classifier gradients. The approach guarantees a single, simply connected mask, cuts the number of free parameters by orders of magnitude, and yields stable boundary updates without cleanup. Restricting solutions to low-dimensional, smooth contours makes the method robust to adversarial masking artifacts. On ImageNet classifiers, it matches the extremal fidelity of dense masks while producing compact, interpretable regions with improved run-to-run consistency. Explicit area control also enables importance contour maps, yielding a transparent fidelity area profiles. Finally, we extend the approach to multi-contour and show how it can localize multiple objects within the same framework. Across benchmarks, the method achieves higher relevance mass and lower complexity than gradient and perturbation based baselines, with especially strong gains on self-supervised DINO models where it improves relevance mass by over 15% and maintains positive faithfulness correlations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v307-karimzadeh26a, title = {Extremal Contours: Gradient-driven contours for compact visual attribution}, author = {Karimzadeh, Reza and Alonso, Albert and Zdyb, Frans and Kirkegaard, Julius B. and Ibragimov, Bulat}, booktitle = {Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL)}, pages = {201--210}, year = {2026}, editor = {Kim, Hyeongji and Ramírez Rivera, Adín and Ricaud, Benjamin}, volume = {307}, series = {Proceedings of Machine Learning Research}, month = {06--08 Jan}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v307/main/assets/karimzadeh26a/karimzadeh26a.pdf}, url = {https://proceedings.mlr.press/v307/karimzadeh26a.html}, abstract = {Faithful yet compact explanations for vision models remain a challenge, as commonly used dense perturbation masks are often fragmented and overfitted, needing careful post-processing. Here, we present a training-free explanation method that replaces dense masks with smooth tunable contours. A star-convex region is parameterized by a truncated Fourier series and optimized under an extremal preserve/delete objective using the classifier gradients. The approach guarantees a single, simply connected mask, cuts the number of free parameters by orders of magnitude, and yields stable boundary updates without cleanup. Restricting solutions to low-dimensional, smooth contours makes the method robust to adversarial masking artifacts. On ImageNet classifiers, it matches the extremal fidelity of dense masks while producing compact, interpretable regions with improved run-to-run consistency. Explicit area control also enables importance contour maps, yielding a transparent fidelity area profiles. Finally, we extend the approach to multi-contour and show how it can localize multiple objects within the same framework. Across benchmarks, the method achieves higher relevance mass and lower complexity than gradient and perturbation based baselines, with especially strong gains on self-supervised DINO models where it improves relevance mass by over 15% and maintains positive faithfulness correlations.} }
Endnote
%0 Conference Paper %T Extremal Contours: Gradient-driven contours for compact visual attribution %A Reza Karimzadeh %A Albert Alonso %A Frans Zdyb %A Julius B. Kirkegaard %A Bulat Ibragimov %B Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL) %C Proceedings of Machine Learning Research %D 2026 %E Hyeongji Kim %E Adín Ramírez Rivera %E Benjamin Ricaud %F pmlr-v307-karimzadeh26a %I PMLR %P 201--210 %U https://proceedings.mlr.press/v307/karimzadeh26a.html %V 307 %X Faithful yet compact explanations for vision models remain a challenge, as commonly used dense perturbation masks are often fragmented and overfitted, needing careful post-processing. Here, we present a training-free explanation method that replaces dense masks with smooth tunable contours. A star-convex region is parameterized by a truncated Fourier series and optimized under an extremal preserve/delete objective using the classifier gradients. The approach guarantees a single, simply connected mask, cuts the number of free parameters by orders of magnitude, and yields stable boundary updates without cleanup. Restricting solutions to low-dimensional, smooth contours makes the method robust to adversarial masking artifacts. On ImageNet classifiers, it matches the extremal fidelity of dense masks while producing compact, interpretable regions with improved run-to-run consistency. Explicit area control also enables importance contour maps, yielding a transparent fidelity area profiles. Finally, we extend the approach to multi-contour and show how it can localize multiple objects within the same framework. Across benchmarks, the method achieves higher relevance mass and lower complexity than gradient and perturbation based baselines, with especially strong gains on self-supervised DINO models where it improves relevance mass by over 15% and maintains positive faithfulness correlations.
APA
Karimzadeh, R., Alonso, A., Zdyb, F., Kirkegaard, J.B. & Ibragimov, B.. (2026). Extremal Contours: Gradient-driven contours for compact visual attribution. Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), in Proceedings of Machine Learning Research 307:201-210 Available from https://proceedings.mlr.press/v307/karimzadeh26a.html.

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