# H-Sets: Hessian-Guided Discovery of Set-Level Feature Interactions in Image Classifiers

arXiv: https://arxiv.org/abs/2604.22045 · HTML: https://mlsanity.com/paper/2604.22045/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (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)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [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)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Quantus: An Explainable AI Toolkit for Responsible Evaluation of Neural Network Explanations and Beyond](https://mlsanity.com/paper/2202.06861/) (2022)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [A Consistent and Efficient Evaluation Strategy for Attribution Methods](https://mlsanity.com/paper/2202.00449/) (2022)
- [Interpretable Deep Learning under Fire](https://mlsanity.com/paper/1812.00891/) (2018)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Hierarchical interpretations for neural network predictions](https://mlsanity.com/paper/1806.05337/) (2018)
- [Understanding Impacts of High-Order Loss Approximations and Features in Deep Learning Interpretation](https://mlsanity.com/paper/1902.00407/) (2019)
- [PredDiff: Explanations and Interactions from Conditional Expectations](https://mlsanity.com/paper/2102.13519/) (2021)
- [Learning to Understand: Identifying Interactions via the M"obius Transform](https://mlsanity.com/paper/2402.02631/) (2024)

## Built on by (most cited first, 1 of 1)

- [The Representational Limit of Scalar Interactions: An Interventional Decomposition](https://mlsanity.com/paper/2606.19410/) (2026)

## Abstract (arXiv)

Feature attribution methods explain the predictions of deep neural networks by assigning importance scores to individual input features. However, most existing methods focus solely on marginal effects, overlooking feature interactions, where groups of features jointly influence model output. Such interactions are especially important in image classification tasks, where semantic meaning often arises from pixel interdependencies rather than isolated features. Existing interaction-based methods for images are either coarse (e.g., superpixel-only) or, fail to satisfy core interpretability axioms. In this work, we introduce H-Sets, a novel two-stage framework for discovering and attributing higher-order feature interactions in image classifiers. First, we detect locally interacting pairs via input Hessians and recursively merge them into semantically coherent sets; segmentation from Segment Anything (SAM) is used as a spatial grouping prior but can be replaced by other segmentations. Second, we attribute each set with IDG-Vis, a set-level extension of Integrated Directional Gradients that integrates directional gradients along pixel-space paths and aggregates them with Harsanyi dividends. While Hessians introduce additional compute at the detection stage, this targeted cost consistently yields saliency maps that are sparser and more faithful. Evaluations across VGG, ResNet, DenseNet and MobileNet models on ImageNet and CUB datasets show that H-Sets generate more interpretable and faithful saliency maps compared to existing methods.