# Mutual Information Preserving Back-propagation: Learn to Invert for Faithful Attribution

arXiv: https://arxiv.org/abs/2104.06629 · HTML: https://mlsanity.com/paper/2104.06629/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 28 of 28)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [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)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [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)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [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)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Restricting the Flow: Information Bottlenecks for Attribution](https://mlsanity.com/paper/2001.00396/) (2020)
- [When Explanations Lie: Why Many Modified BP Attributions Fail](https://mlsanity.com/paper/1912.09818/) (2019)
- [Learning how to explain neural networks: PatternNet and PatternAttribution](https://mlsanity.com/paper/1705.05598/) (2017)
- [A Theoretical Explanation for Perplexing Behaviors of Backpropagation-based Visualizations](https://mlsanity.com/paper/1805.07039/) (2018)
- [iNNvestigate neural networks!](https://mlsanity.com/paper/1808.04260/) (2018)
- [Interpretable and Fine-Grained Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1908.02686/) (2019)
- [Explaining Deep Neural Networks and Beyond: A Review of Methods and Applications](https://mlsanity.com/paper/2003.07631/) (2020)
- [A Unified Taylor Framework for Revisiting Attribution Methods](https://mlsanity.com/paper/2008.09695/) (2020)

## Built on by (most cited first, 3 of 3)

- [HarsanyiNet: Computing Accurate Shapley Values in a Single Forward Propagation](https://mlsanity.com/paper/2304.01811/) (2023)
- [Understanding and Unifying Fourteen Attribution Methods with Taylor Interactions](https://mlsanity.com/paper/2303.01506/) (2023)
- [Attribution Explanations for Deep Neural Networks: A Theoretical Perspective](https://mlsanity.com/paper/2508.07636/) (2025)

## Abstract (arXiv)

Back propagation based visualizations have been proposed to interpret deep neural networks (DNNs), some of which produce interpretations with good visual quality. However, there exist doubts about whether these intuitive visualizations are related to the network decisions. Recent studies have confirmed this suspicion by verifying that almost all these modified back-propagation visualizations are not faithful to the model's decision-making process. Besides, these visualizations produce vague "relative importance scores", among which low values can't guarantee to be independent of the final prediction. Hence, it's highly desirable to develop a novel back-propagation framework that guarantees theoretical faithfulness and produces a quantitative attribution score with a clear understanding. To achieve the goal, we resort to mutual information theory to generate the interpretations, studying how much information of output is encoded in each input neuron. The basic idea is to learn a source signal by back-propagation such that the mutual information between input and output should be as much as possible preserved in the mutual information between input and the source signal. In addition, we propose a Mutual Information Preserving Inverse Network, termed MIP-IN, in which the parameters of each layer are recursively trained to learn how to invert. During the inversion, forward Relu operation is adopted to adapt the general interpretations to the specific input. We then empirically demonstrate that the inverted source signal satisfies completeness and minimality property, which are crucial for a faithful interpretation. Furthermore, the empirical study validates the effectiveness of interpretations generated by MIP-IN.