mlsanityData to 7 Oct 2026

Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation

arXiv 1903.10992 ↗First posted 26 Mar 2019cs.LG stat.MLcited by 115

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Abstract (arXiv)

The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about their reliability. On the other hand, the literature on cooperative game theory suggests Shapley values as a unique way of assigning relevance scores such that certain desirable properties are satisfied. Unfortunately, the exact evaluation of Shapley values is prohibitively expensive, exponential in the number of input features. In this work, by leveraging recent results on uncertainty propagation, we propose a novel, polynomial-time approximation of Shapley values in deep neural networks. We show that our method produces significantly better approximations of Shapley values than existing state-of-the-art attribution methods.

Key facts. Cited by 115 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Mar 2019.

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Citing papers per year: 2021: 37; 2022: 18; 2023: 24; 2024: 19; 2025: 9; 2026: 8.

115 papers.

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  1. 2022From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AIcited by 299
  2. 2021FastSHAP: Real-Time Shapley Value Estimationcited by 123
  3. 2022Algorithms to estimate Shapley value feature attributionscited by 114
  4. 2022The Shapley Value in Machine Learningcited by 97
  5. 2021Synthetic Benchmarks for Scientific Research in Explainable Machine Learningcited by 59
  6. 2022MogaNet: Multi-order Gated Aggregation Networkcited by 59
  7. 2024Explainable Artificial Intelligence: A Survey of Needs, Techniques, Applications, and Future Directioncited by 46
  8. 2021Explainability-based Backdoor Attacks Against Graph Neural Networkscited by 42
  9. 2021Discovering and Explaining the Representation Bottleneck of DNNscited by 42
  10. 2021Shapley Explanation Networkscited by 41
  11. 2021Explaining a Series of Models by Propagating Shapley Valuescited by 37
  12. 2021Shapley Counterfactual Credits for Multi-Agent Reinforcement Learningcited by 37
38 more
  1. 2023Explain Any Concept: Segment Anything Meets Concept-Based Explanationcited by 37
  2. 2021Defining and Quantifying the Emergence of Sparse Concepts in DNNscited by 36
  3. 2022Explaining Deepfake Detection by Analysing Image Matchingcited by 34
  4. 2023Approximating the Shapley Value without Marginal Contributionscited by 34
  5. 2023LINe: Out-of-Distribution Detection by Leveraging Important Neuronscited by 34
  6. 2021Neural Response Interpretation through the Lens of Critical Pathwayscited by 32
  7. 2022Architecture-Agnostic Masked Image Modeling -- From ViT back to CNNcited by 31
  8. 2021Toward Explainable AI for Regression Modelscited by 30
  9. 2022Repairing Neural Networks by Leaving the Right Past Behindcited by 27
  10. 2022Interpretable Geometric Deep Learning via Learnable Randomness Injectioncited by 27
  11. 2023Does a Neural Network Really Encode Symbolic Concepts?cited by 27
  12. 2021SHAQ: Incorporating Shapley Value Theory into Multi-Agent Q-Learningcited by 26
  13. 2021The Shapley Value of Classifiers in Ensemble Gamescited by 23
  14. 2021You Mostly Walk Alone: Analyzing Feature Attribution in Trajectory Predictioncited by 23
  15. 2022Shapley-NAS: Discovering Operation Contribution for Neural Architecture Searchcited by 23
  16. 2021Best of both worlds: local and global explanations with human-understandable conceptscited by 22
  17. 2021Interpretable deep-learning models to help achieve the Sustainable Development Goalscited by 18
  18. 2021A Unified Game-Theoretic Interpretation of Adversarial Robustnesscited by 17
  19. 2021A Game-Theoretic Taxonomy of Visual Concepts in DNNscited by 16
  20. 2023HarsanyiNet: Computing Accurate Shapley Values in a Single Forward Propagationcited by 16
  21. 2021Explainable Deep Learning in Healthcare: A Methodological Survey from an Attribution Viewcited by 15
  22. 2023A Comparative Study of Methods for Estimating Conditional Shapley Values and When to Use Themcited by 15
  23. 2023Efficient XAI Techniques: A Taxonomic Surveycited by 14
  24. 2022Accelerating Shapley Explanation via Contributive Cooperator Selectioncited by 13
  25. 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanationscited by 13
  26. 2021Interpreting Representation Quality of DNNs for 3D Point Cloud Processingcited by 12
  27. 2023Shapley Values-enabled Progressive Pseudo Bag Augmentation for Whole Slide Image Classificationcited by 12
  28. 2024IG2: Integrated Gradient on Iterative Gradient Path for Feature Attributioncited by 12
  29. 2021Can We Faithfully Represent Masked States to Compute Shapley Values on a DNN?cited by 10
  30. 2021Energy-Based Learning for Cooperative Games, with Applications to Valuation Problems in Machine Learningcited by 10
  31. 2021Multi-objective Explanations of GNN Predictionscited by 10
  32. 2023Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNscited by 10
  33. 2023Keep the Faith: Faithful Explanations in Convolutional Neural Networks for Case-Based Reasoningcited by 10
  34. 2021Instance-wise or Class-wise? A Tale of Neighbor Shapley for Concept-based Explanationcited by 9
  35. 2023Bayesian Neural Networks Avoid Encoding Complex and Perturbation-Sensitive Conceptscited by 9
  36. 2024Feature Inference Attack on Shapley Valuescited by 9
  37. 2021Ensembles of Random SHAPscited by 8
  38. 2022Cardinality-Minimal Explanations for Monotonic Neural Networkscited by 8

50 most cited of 115 All 115 (JSON)