# Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?

arXiv: https://arxiv.org/abs/2106.02890 · HTML: https://mlsanity.com/paper/2106.02890/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 91 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 30 of 63)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)

## Built on by (most cited first, 30 of 75)

- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Task-Specific Skill Localization in Fine-tuned Language Models](https://mlsanity.com/paper/2302.06600/) (2023)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [Head2Toe: Utilizing Intermediate Representations for Better Transfer Learning](https://mlsanity.com/paper/2201.03529/) (2022)
- [Agree to Disagree: Diversity through Disagreement for Better Transferability](https://mlsanity.com/paper/2202.04414/) (2022)
- [A Winning Hand: Compressing Deep Networks Can Improve Out-Of-Distribution Robustness](https://mlsanity.com/paper/2106.09129/) (2021)
- [Model Agnostic Sample Reweighting for Out-of-Distribution Learning](https://mlsanity.com/paper/2301.09819/) (2023)
- [Break It Down: Evidence for Structural Compositionality in Neural Networks](https://mlsanity.com/paper/2301.10884/) (2023)
- [Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlations](https://mlsanity.com/paper/2107.00520/) (2021)
- [Fortuitous Forgetting in Connectionist Networks](https://mlsanity.com/paper/2202.00155/) (2022)
- [NAS-OoD: Neural Architecture Search for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02038/) (2021)
- [Sparsity May Cry: Let Us Fail (Current) Sparse Neural Networks Together!](https://mlsanity.com/paper/2303.02141/) (2023)
- [Sparse Double Descent: Where Network Pruning Aggravates Overfitting](https://mlsanity.com/paper/2206.08684/) (2022)
- [Spurious Feature Diversification Improves Out-of-distribution Generalization](https://mlsanity.com/paper/2309.17230/) (2023)
- [Distribution Shift Inversion for Out-of-Distribution Prediction](https://mlsanity.com/paper/2306.08328/) (2023)
- [Configurable Foundation Models: Building LLMs from a Modular Perspective](https://mlsanity.com/paper/2409.02877/) (2024)
- [DomainDrop: Suppressing Domain-Sensitive Channels for Domain Generalization](https://mlsanity.com/paper/2308.10285/) (2023)
- [Uncertainty-Calibrated Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2403.11491/) (2024)
- [Learning Transferable Parameters for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2108.06129/) (2021)
- [Exploring Optimal Substructure for Out-of-distribution Generalization via Feature-targeted Model Pruning](https://mlsanity.com/paper/2212.09458/) (2022)
- [Training Debiased Subnetworks with Contrastive Weight Pruning](https://mlsanity.com/paper/2210.05247/) (2022)
- [Robust Lottery Tickets for Pre-trained Language Models](https://mlsanity.com/paper/2211.03013/) (2022)
- [Stochastic Parameter Decomposition](https://mlsanity.com/paper/2506.20790/) (2025)
- [Towards Artificial General Intelligence (AGI) in the Internet of Things (IoT): Opportunities and Challenges](https://mlsanity.com/paper/2309.07438/) (2023)
- [Sheaf Discovery with Joint Computation Graph Pruning and Flexible Granularity](https://mlsanity.com/paper/2407.03779/) (2024)
- [Winning Prize Comes from Losing Tickets: Improve Invariant Learning by Exploring Variant Parameters for Out-of-Distribution Generalization](https://mlsanity.com/paper/2310.16391/) (2023)
- [Uncovering Intermediate Variables in Transformers using Circuit Probing](https://mlsanity.com/paper/2311.04354/) (2023)

## Abstract (arXiv)

Can models with particular structure avoid being biased towards spurious correlation in out-of-distribution (OOD) generalization? Peters et al. (2016) provides a positive answer for linear cases. In this paper, we use a functional modular probing method to analyze deep model structures under OOD setting. We demonstrate that even in biased models (which focus on spurious correlation) there still exist unbiased functional subnetworks. Furthermore, we articulate and demonstrate the functional lottery ticket hypothesis: full network contains a subnetwork that can achieve better OOD performance. We then propose Modular Risk Minimization to solve the subnetwork selection problem. Our algorithm learns the subnetwork structure from a given dataset, and can be combined with any other OOD regularization methods. Experiments on various OOD generalization tasks corroborate the effectiveness of our method.