# Understanding and Unifying Fourteen Attribution Methods with Taylor Interactions

arXiv: https://arxiv.org/abs/2303.01506 · HTML: https://mlsanity.com/paper/2303.01506/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 24 of 24)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (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)
- ["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)
- [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)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [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)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Restricting the Flow: Information Bottlenecks for Attribution](https://mlsanity.com/paper/2001.00396/) (2020)
- [A Theoretical Explanation for Perplexing Behaviors of Backpropagation-based Visualizations](https://mlsanity.com/paper/1805.07039/) (2018)
- [Improving performance of deep learning models with axiomatic attribution priors and expected gradients](https://mlsanity.com/paper/1906.10670/) (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)
- [Mutual Information Preserving Back-propagation: Learn to Invert for Faithful Attribution](https://mlsanity.com/paper/2104.06629/) (2021)

## Built on by (most cited first, 11 of 11)

- [Language Modeling on Tabular Data: A Survey of Foundations, Techniques and Evolution](https://mlsanity.com/paper/2408.10548/) (2024)
- [Defining and Extracting generalizable interaction primitives from DNNs](https://mlsanity.com/paper/2401.16318/) (2024)
- [Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs](https://mlsanity.com/paper/2304.13312/) (2023)
- [GAIA: Delving into Gradient-based Attribution Abnormality for Out-of-distribution Detection](https://mlsanity.com/paper/2311.09620/) (2023)
- [Can the Inference Logic of Large Language Models be Disentangled into Symbolic Concepts?](https://mlsanity.com/paper/2304.01083/) (2023)
- [Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models](https://mlsanity.com/paper/2305.01939/) (2023)
- [Neuron Patching: Semantic-based Neuron-level Language Model Repair for Code Generation](https://mlsanity.com/paper/2312.05356/) (2023)
- [On the Evaluation Consistency of Attribution-based Explanations](https://mlsanity.com/paper/2407.19471/) (2024)
- [A Semantic-based Optimization Approach for Repairing LLMs: Case Study on Code Generation](https://mlsanity.com/paper/2503.12899/) (2025)
- [The Weighted M"obius Score: A Unified Framework for Feature Attribution](https://mlsanity.com/paper/2305.09204/) (2023)
- [Manifold-based Shapley for SAR Recognization Network Explanation](https://mlsanity.com/paper/2401.03128/) (2024)

## Abstract (arXiv)

Various attribution methods have been developed to explain deep neural networks (DNNs) by inferring the attribution/importance/contribution score of each input variable to the final output. However, existing attribution methods are often built upon different heuristics. There remains a lack of a unified theoretical understanding of why these methods are effective and how they are related. To this end, for the first time, we formulate core mechanisms of fourteen attribution methods, which were designed on different heuristics, into the same mathematical system, i.e., the system of Taylor interactions. Specifically, we prove that attribution scores estimated by fourteen attribution methods can all be reformulated as the weighted sum of two types of effects, i.e., independent effects of each individual input variable and interaction effects between input variables. The essential difference among the fourteen attribution methods mainly lies in the weights of allocating different effects. Based on the above findings, we propose three principles for a fair allocation of effects to evaluate the faithfulness of the fourteen attribution methods.