# Spuriosity Didn't Kill the Classifier: Using Invariant Predictions to Harness Spurious Features

arXiv: https://arxiv.org/abs/2307.09933 · HTML: https://mlsanity.com/paper/2307.09933/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 91 references that are in the map.
- First posted on arXiv 19 Jul 2023.

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

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [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)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Learning from Noisy Labels with Distillation](https://mlsanity.com/paper/1703.02391/) (2017)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Exploiting Domain-Specific Features to Enhance Domain Generalization](https://mlsanity.com/paper/2110.09410/) (2021)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)

## Built on by (most cited first, 21 of 21)

- [The Clever Hans Mirage: A Comprehensive Survey on Spurious Correlations in Machine Learning](https://mlsanity.com/paper/2402.12715/) (2024)
- [Discovering environments with XRM](https://mlsanity.com/paper/2309.16748/) (2023)
- [On Provable Length and Compositional Generalization](https://mlsanity.com/paper/2402.04875/) (2024)
- [Domain Generalisation via Imprecise Learning](https://mlsanity.com/paper/2404.04669/) (2024)
- [Accuracy on the wrong line: On the pitfalls of noisy data for out-of-distribution generalisation](https://mlsanity.com/paper/2406.19049/) (2024)
- [Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2411.19923/) (2024)
- [When Shift Happens - Confounding Is to Blame](https://mlsanity.com/paper/2505.21422/) (2025)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2402.09165/) (2024)
- [Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2407.15273/) (2024)
- [Adapting to Shifting Correlations with Unlabeled Data Calibration](https://mlsanity.com/paper/2409.05996/) (2024)
- [Bridging Distribution Shift and AI Safety: Conceptual and Methodological Synergies](https://mlsanity.com/paper/2505.22829/) (2025)
- [Context is Environment](https://mlsanity.com/paper/2309.09888/) (2023)
- [Single-weight Model Editing for Post-hoc Spurious Correlation Neutralization](https://mlsanity.com/paper/2501.14182/) (2025)
- [Trust Me, I Know the Way: Predictive Uncertainty in the Presence of Shortcut Learning](https://mlsanity.com/paper/2502.09137/) (2025)
- [SCL-GNN: Towards Generalizable Graph Neural Networks via Spurious Correlation Learning](https://mlsanity.com/paper/2603.08270/) (2026)
- [Spurious Correlations in Concept Drift: Can Explanatory Interaction Help?](https://mlsanity.com/paper/2407.16515/) (2024)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [Transferring Causal Effects using Proxies](https://mlsanity.com/paper/2510.25924/) (2025)
- [Anti-causal domain generalization: Leveraging unlabeled data](https://mlsanity.com/paper/2602.17187/) (2026)
- [Why Invariance is Not Enough for Biomedical Domain Generalization and How to Fix It](https://mlsanity.com/paper/2604.02564/) (2026)

## Abstract (arXiv)

To avoid failures on out-of-distribution data, recent works have sought to extract features that have an invariant or stable relationship with the label across domains, discarding "spurious" or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information that could boost performance if used correctly in the test domain. In this work, we show how this can be done without test-domain labels. In particular, we prove that pseudo-labels based on stable features provide sufficient guidance for doing so, provided that stable and unstable features are conditionally independent given the label. Based on this theoretical insight, we propose Stable Feature Boosting (SFB), an algorithm for: (i) learning a predictor that separates stable and conditionally-independent unstable features; and (ii) using the stable-feature predictions to adapt the unstable-feature predictions in the test domain. Theoretically, we prove that SFB can learn an asymptotically-optimal predictor without test-domain labels. Empirically, we demonstrate the effectiveness of SFB on real and synthetic data.