# Extremal Contours: Gradient-driven contours for compact visual attribution

arXiv: https://arxiv.org/abs/2511.01411 · HTML: https://mlsanity.com/paper/2511.01411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 27 of 27)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Ground Truth Evaluation of Neural Network Explanations with CLEVR-XAI](https://mlsanity.com/paper/2003.07258/) (2020)
- [Restricting the Flow: Information Bottlenecks for Attribution](https://mlsanity.com/paper/2001.00396/) (2020)
- [RELAX: Representation Learning Explainability](https://mlsanity.com/paper/2112.10161/) (2021)
- [Fast spline detection in high density microscopy data](https://mlsanity.com/paper/2301.04460/) (2023)
- [Spline refinement with differentiable rendering](https://mlsanity.com/paper/2503.14525/) (2025)
- [Towards Voronoi Diagrams of Surface Patches](https://mlsanity.com/paper/2411.06471/) (2024)
- [Generating visual explanations from deep networks using implicit neural representations](https://mlsanity.com/paper/2501.11784/) (2025)

## Abstract (arXiv)

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.