# Negative Flux Aggregation to Estimate Feature Attributions

arXiv: https://arxiv.org/abs/2301.06989 · HTML: https://mlsanity.com/paper/2301.06989/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 17 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (2019)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [Do Input Gradients Highlight Discriminative Features?](https://mlsanity.com/paper/2102.12781/) (2021)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [Fast Axiomatic Attribution for Neural Networks](https://mlsanity.com/paper/2111.07668/) (2021)
- [Investigating Saturation Effects in Integrated Gradients](https://mlsanity.com/paper/2010.12697/) (2020)
- [Improving Adversarial Robustness via Probabilistically Compact Loss with Logit Constraints](https://mlsanity.com/paper/2012.07688/) (2020)
- [Explainable Recommendation via Interpretable Feature Mapping and Evaluation of Explainability](https://mlsanity.com/paper/2007.06133/) (2020)

## Built on by (most cited first, 7 of 7)

- [Gradient based Feature Attribution in Explainable AI: A Technical Review](https://mlsanity.com/paper/2403.10415/) (2024)
- [Facial Affective Behavior Analysis with Instruction Tuning](https://mlsanity.com/paper/2404.05052/) (2024)
- [Interpretability-Aware Vision Transformer](https://mlsanity.com/paper/2309.08035/) (2023)
- [Fairness-aware Vision Transformer via Debiased Self-Attention](https://mlsanity.com/paper/2301.13803/) (2023)
- [QUCE: The Minimisation and Quantification of Path-Based Uncertainty for Generative Counterfactual Explanations](https://mlsanity.com/paper/2402.17516/) (2024)
- [Enhancing Interpretability for Vision Models via Shapley Value Optimization](https://mlsanity.com/paper/2512.14354/) (2025)
- [Fast Explanations via Policy Gradient-Optimized Explainer](https://mlsanity.com/paper/2405.18664/) (2024)

## Abstract (arXiv)

There are increasing demands for understanding deep neural networks' (DNNs) behavior spurred by growing security and/or transparency concerns. Due to multi-layer nonlinearity of the deep neural network architectures, explaining DNN predictions still remains as an open problem, preventing us from gaining a deeper understanding of the mechanisms. To enhance the explainability of DNNs, we estimate the input feature's attributions to the prediction task using divergence and flux. Inspired by the divergence theorem in vector analysis, we develop a novel Negative Flux Aggregation (NeFLAG) formulation and an efficient approximation algorithm to estimate attribution map. Unlike the previous techniques, ours doesn't rely on fitting a surrogate model nor need any path integration of gradients. Both qualitative and quantitative experiments demonstrate a superior performance of NeFLAG in generating more faithful attribution maps than the competing methods. Our code is available at urlhttps://github.com/xinli0928/NeFLAG