# Shapley-NAS: Discovering Operation Contribution for Neural Architecture Search

arXiv: https://arxiv.org/abs/2206.09811 · HTML: https://mlsanity.com/paper/2206.09811/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 51 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search](https://mlsanity.com/paper/1907.05737/) (2019)
- [Searching for A Robust Neural Architecture in Four GPU Hours](https://mlsanity.com/paper/1910.04465/) (2019)
- [Random Search and Reproducibility for Neural Architecture Search](https://mlsanity.com/paper/1902.07638/) (2019)
- [Progressive Differentiable Architecture Search: Bridging the Depth Gap between Search and Evaluation](https://mlsanity.com/paper/1904.12760/) (2019)
- [Understanding and Robustifying Differentiable Architecture Search](https://mlsanity.com/paper/1909.09656/) (2019)
- [Neural Architecture Optimization](https://mlsanity.com/paper/1808.07233/) (2018)
- [Evaluating the Search Phase of Neural Architecture Search](https://mlsanity.com/paper/1902.08142/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Stabilizing Differentiable Architecture Search via Perturbation-based Regularization](https://mlsanity.com/paper/2002.05283/) (2020)

## Built on by (most cited first, 23 of 23)

- [Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration](https://mlsanity.com/paper/2403.04629/) (2024)
- [Construction of Hierarchical Neural Architecture Search Spaces based on Context-free Grammars](https://mlsanity.com/paper/2211.01842/) (2022)
- [MCUFormer: Deploying Vision Transformers on Microcontrollers with Limited Memory](https://mlsanity.com/paper/2310.16898/) (2023)
- [SEKI: Self-Evolution and Knowledge Inspiration based Neural Architecture Search via Large Language Models](https://mlsanity.com/paper/2502.20422/) (2025)
- [Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining](https://mlsanity.com/paper/2308.06755/) (2023)
- [Robustifying and Boosting Training-Free Neural Architecture Search](https://mlsanity.com/paper/2403.07591/) (2024)
- [OStr-DARTS: Differentiable Neural Architecture Search based on Operation Strength](https://mlsanity.com/paper/2409.14433/) (2024)
- [Multi-Agent Automated Machine Learning](https://mlsanity.com/paper/2210.09084/) (2022)
- [Automated Dominative Subspace Mining for Efficient Neural Architecture Search](https://mlsanity.com/paper/2210.17180/) (2022)
- [LayerNAS: Neural Architecture Search in Polynomial Complexity](https://mlsanity.com/paper/2304.11517/) (2023)
- [GeNAS: Neural Architecture Search with Better Generalization](https://mlsanity.com/paper/2305.08611/) (2023)
- [Search-time Efficient Device Constraints-Aware Neural Architecture Search](https://mlsanity.com/paper/2307.04443/) (2023)
- [A Pairwise Comparison Relation-assisted Multi-objective Evolutionary Neural Architecture Search Method with Multi-population Mechanism](https://mlsanity.com/paper/2407.15600/) (2024)
- [CARL: Causality-guided Architecture Representation Learning for an Interpretable Performance Predictor](https://mlsanity.com/paper/2506.04001/) (2025)
- [Using Cooperative Game Theory to Prune Neural Networks](https://mlsanity.com/paper/2311.10468/) (2023)
- [In-Distribution Consistency Regularization Improves the Generalization of Quantization-Aware Training](https://mlsanity.com/paper/2402.13497/) (2024)
- [DDS-NAS: Dynamic Data Selection within Neural Architecture Search via On-line Hard Example Mining applied to Image Classification](https://mlsanity.com/paper/2506.14667/) (2025)
- [Where and How to Enhance: Discovering Bit-Width Contribution for Mixed Precision Quantization](https://mlsanity.com/paper/2508.03002/) (2025)
- [MGAS: Multi-Granularity Architecture Search for Trade-Off Between Model Effectiveness and Efficiency](https://mlsanity.com/paper/2310.15074/) (2023)
- [BSS-Bench: Towards Reproducible and Effective Band Selection Search](https://mlsanity.com/paper/2312.14570/) (2023)
- [Neural Architecture Search by Learning a Hierarchical Search Space](https://mlsanity.com/paper/2503.21061/) (2025)
- [OptiProxy-NAS: Optimization Proxy based End-to-End Neural Architecture Search](https://mlsanity.com/paper/2509.05656/) (2025)
- [Hybrid-LoRA: Bridging Full Fine-Tuning and Low-Rank Adaptation for Post-Training](https://mlsanity.com/paper/2605.18822/) (2026)

## Abstract (arXiv)

In this paper, we propose a Shapley value based method to evaluate operation contribution (Shapley-NAS) for neural architecture search. Differentiable architecture search (DARTS) acquires the optimal architectures by optimizing the architecture parameters with gradient descent, which significantly reduces the search cost. However, the magnitude of architecture parameters updated by gradient descent fails to reveal the actual operation importance to the task performance and therefore harms the effectiveness of obtained architectures. By contrast, we propose to evaluate the direct influence of operations on validation accuracy. To deal with the complex relationships between supernet components, we leverage Shapley value to quantify their marginal contributions by considering all possible combinations. Specifically, we iteratively optimize the supernet weights and update the architecture parameters by evaluating operation contributions via Shapley value, so that the optimal architectures are derived by selecting the operations that contribute significantly to the tasks. Since the exact computation of Shapley value is NP-hard, the Monte-Carlo sampling based algorithm with early truncation is employed for efficient approximation, and the momentum update mechanism is adopted to alleviate fluctuation of the sampling process. Extensive experiments on various datasets and various search spaces show that our Shapley-NAS outperforms the state-of-the-art methods by a considerable margin with light search cost. The code is available at https://github.com/Euphoria16/Shapley-NAS.git