# HarsanyiNet: Computing Accurate Shapley Values in a Single Forward Propagation

arXiv: https://arxiv.org/abs/2304.01811 · HTML: https://mlsanity.com/paper/2304.01811/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 60 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 30 of 40)

- [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)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (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)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (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)
- [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)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [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)
- [ResNet strikes back: An improved training procedure in timm](https://mlsanity.com/paper/2110.00476/) (2021)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [COVID-Net: A Tailored Deep Convolutional Neural Network Design for Detection of COVID-19 Cases from Chest X-Ray Images](https://mlsanity.com/paper/2003.09871/) (2020)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Restricting the Flow: Information Bottlenecks for Attribution](https://mlsanity.com/paper/2001.00396/) (2020)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)

## Built on by (most cited first, 17 of 17)

- [Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs](https://mlsanity.com/paper/2304.13312/) (2023)
- [INTER: Mitigating Hallucination in Large Vision-Language Models by Interaction Guidance Sampling](https://mlsanity.com/paper/2507.05056/) (2025)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Diagnosing the Compositional Knowledge of Vision Language Models from a Game-Theoretic View](https://mlsanity.com/paper/2405.17201/) (2024)
- [Generalized Attention Flow: Feature Attribution for Transformer Models via Maximum Flow](https://mlsanity.com/paper/2502.15765/) (2025)
- [Prediction via Shapley Value Regression](https://mlsanity.com/paper/2505.04775/) (2025)
- [Fast Shapley Value Estimation: A Unified Approach](https://mlsanity.com/paper/2311.01010/) (2023)
- [A Survey on Interpretability in Visual Recognition](https://mlsanity.com/paper/2507.11099/) (2025)
- [Composing Linear Layers from Irreducibles](https://mlsanity.com/paper/2507.11688/) (2025)
- [Enhancing Interpretability for Vision Models via Shapley Value Optimization](https://mlsanity.com/paper/2512.14354/) (2025)
- [TVE: Learning Meta-attribution for Transferable Vision Explainer](https://mlsanity.com/paper/2312.15359/) (2023)
- [Is Data Valuation Learnable and Interpretable?](https://mlsanity.com/paper/2406.02612/) (2024)
- [More Is Not Always Better: Cross-Component Interference in LLM Agent Scaffolding](https://mlsanity.com/paper/2605.05716/) (2026)
- [PhaseWin: An Efficient Search Algorithm for Faithful Visual Attribution](https://mlsanity.com/paper/2606.18008/) (2026)
- [Beyond Models! Explainable Data Valuation and Metric Adaption for Recommendation](https://mlsanity.com/paper/2502.08685/) (2025)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [Do ResNets Route? Sparse Interaction Experts in Residual Networks](https://mlsanity.com/paper/2610.02907/) (2026)

## Abstract (arXiv)

The Shapley value is widely regarded as a trustworthy attribution metric. However, when people use Shapley values to explain the attribution of input variables of a deep neural network (DNN), it usually requires a very high computational cost to approximate relatively accurate Shapley values in real-world applications. Therefore, we propose a novel network architecture, the HarsanyiNet, which makes inferences on the input sample and simultaneously computes the exact Shapley values of the input variables in a single forward propagation. The HarsanyiNet is designed on the theoretical foundation that the Shapley value can be reformulated as the redistribution of Harsanyi interactions encoded by the network.