# Separating Shortcut Transition from Cross-Family OOD Failure in a Minimal Model

arXiv: https://arxiv.org/abs/2605.12945 · HTML: https://mlsanity.com/paper/2605.12945/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 12 of 12)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Learning from Failure: Training Debiased Classifier from Biased Classifier](https://mlsanity.com/paper/2007.02561/) (2020)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)

## Abstract (arXiv)

Shortcut features are often invoked to explain out-of-distribution (OOD) failure, but training correlation, learned shortcut use, and test-time failure need not coincide. We study a minimal binary model with one invariant coordinate and one family-dependent shortcut coordinate. In the deterministic regime, positive average shortcut correlation pulls logistic ERM toward positive shortcut weight, but ridge regularization keeps the classifier invariant-dominated and prevents deterministic OOD failure. When the invariant coordinate is noisy, ridge-logistic ERM switches to the shortcut rule once the training shortcut signal exceeds the invariant signal. Whether that transition causes failure depends on the held-out family: weaker shortcut correlation yields positive excess risk, and sign-flipped families yield above-chance error. Synthetic checks match these analytic regimes and show that the same training-side transition can have different held-out consequences. The model separates shortcut attraction, shortcut-rule transition, and cross-family OOD failure.