# CAMs as Shapley Value-based Explainers

arXiv: https://arxiv.org/abs/2501.06261 · HTML: https://mlsanity.com/paper/2501.06261/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## 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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Score-CAM: Score-Weighted Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01279/) (2019)
- [Axiom-based Grad-CAM: Towards Accurate Visualization and Explanation of CNNs](https://mlsanity.com/paper/2008.02312/) (2020)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [DataPerf: Benchmarks for Data-Centric AI Development](https://mlsanity.com/paper/2207.10062/) (2022)
- [Explanations in Autonomous Driving: A Survey](https://mlsanity.com/paper/2103.05154/) (2021)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Use HiResCAM instead of Grad-CAM for faithful explanations of convolutional neural networks](https://mlsanity.com/paper/2011.08891/) (2020)
- [Towards Better Explanations of Class Activation Mapping](https://mlsanity.com/paper/2102.05228/) (2021)
- [Revisiting The Evaluation of Class Activation Mapping for Explainability: A Novel Metric and Experimental Analysis](https://mlsanity.com/paper/2104.10252/) (2021)
- [Pre or Post-Softmax Scores in Gradient-based Attribution Methods, What is Best?](https://mlsanity.com/paper/2306.13197/) (2023)
- [Overview of Class Activation Maps for Visualization Explainability](https://mlsanity.com/paper/2309.14304/) (2023)

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

- [Pure Component Property Estimation Framework Using Explainable Machine Learning Methods](https://mlsanity.com/paper/2505.09783/) (2025)
- [Grad-CAM for Visualizing Attention Regions of PCA and SVM Layers in Convolutional Neural Networks](https://mlsanity.com/paper/2508.11880/) (2025)
- [Empirical Evaluation of No Free Lunch Violations in Permutation-Based Optimization](https://mlsanity.com/paper/2603.03613/) (2026)
- [How to Evaluate and Refine your CAM](https://mlsanity.com/paper/2605.14641/) (2026)
- [Class Activation Mapping in Explainable Computer Vision: A Method-Centered Review of CNN, Transformer, and Foundation-Model-Era Visual Explanations](https://mlsanity.com/paper/2608.12299/) (2026)

## Abstract (arXiv)

Class Activation Mapping (CAM) methods are widely used to visualize neural network decisions, yet their underlying mechanisms remain incompletely understood. To enhance the understanding of CAM methods and improve their explainability, we introduce the Content Reserved Game-theoretic (CRG) Explainer. This theoretical framework clarifies the theoretical foundations of GradCAM and HiResCAM by modeling the neural network prediction process as a cooperative game. Within this framework, we develop ShapleyCAM, a new method that leverages gradients and the Hessian matrix to provide more precise and theoretically grounded visual explanations. Due to the computational infeasibility of exact Shapley value calculation, ShapleyCAM employs a second-order Taylor expansion of the cooperative game's utility function to derive a closed-form expression. Additionally, we propose the Residual Softmax Target-Class (ReST) utility function to address the limitations of pre-softmax and post-softmax scores. Extensive experiments across 12 popular networks on the ImageNet validation set demonstrate the effectiveness of ShapleyCAM and its variants. Our findings not only advance CAM explainability but also bridge the gap between heuristic-driven CAM methods and compute-intensive Shapley value-based methods. The code is available at urlhttps://github.com/caihuaiguang/pytorch-shapley-cam.