# Improving Attribution Methods by Learning Submodular Functions

arXiv: https://arxiv.org/abs/2104.09073 · HTML: https://mlsanity.com/paper/2104.09073/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 56 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (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)
- [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)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Interpretable Convolutional Neural Networks](https://mlsanity.com/paper/1710.00935/) (2017)
- [Grad-CAM: Why did you say that?](https://mlsanity.com/paper/1611.07450/) (2016)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (2019)
- [Benchmarking Attribution Methods with Relative Feature Importance](https://mlsanity.com/paper/1907.09701/) (2019)
- [Neural Network Attributions: A Causal Perspective](https://mlsanity.com/paper/1902.02302/) (2019)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Interpretable and Fine-Grained Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1908.02686/) (2019)
- [Smoothed Geometry for Robust Attribution](https://mlsanity.com/paper/2006.06643/) (2020)

## Built on by (most cited first, 5 of 5)

- [Neural Estimation of Submodular Functions with Applications to Differentiable Subset Selection](https://mlsanity.com/paper/2210.11033/) (2022)
- [On the Robustness of Explanations of Deep Neural Network Models: A Survey](https://mlsanity.com/paper/2211.04780/) (2022)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [Provable Robust Saliency-based Explanations](https://mlsanity.com/paper/2212.14106/) (2022)
- [Robust Ranking Explanations](https://mlsanity.com/paper/2307.04024/) (2023)

## Abstract (arXiv)

This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model the principle of diminishing returns. A new formulation for learning a deep submodular set function that is consistent with the real-valued attribution maps obtained by existing attribution methods is proposed. The final attribution value of a feature is then defined as the marginal gain in the induced submodular score of the feature in the context of other highly attributed features, thus decreasing the attribution of redundant yet discriminatory features. Experiments on multiple datasets illustrate that the proposed attribution method achieves higher specificity along with good discriminative power. The implementation of our method is publicly available at https://github.com/Piyushi-0/SEA-NN.