# On the Benefits of Over-parameterization for Out-of-Distribution Generalization

arXiv: https://arxiv.org/abs/2403.17592 · HTML: https://mlsanity.com/paper/2403.17592/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 102 references that are in the map.
- First posted on arXiv 26 Mar 2024.

## Builds on (most cited first, 30 of 64)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)

## Built on by (most cited first, 7 of 7)

- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [Understanding Overadaptation in Supervised Fine-Tuning: The Role of Ensemble Methods](https://mlsanity.com/paper/2506.01901/) (2025)
- [Theoretical Limitations of Ensembles in the Age of Overparameterization](https://mlsanity.com/paper/2410.16201/) (2024)
- [Synergy and Diversity in CLIP: Enhancing Performance Through Adaptive Backbone Ensembling](https://mlsanity.com/paper/2405.17139/) (2024)
- [Scalable Ensemble Diversification for OOD Generalization and Detection](https://mlsanity.com/paper/2409.16797/) (2024)
- [Double Descent Meets Out-of-Distribution Detection: Theoretical Insights and Empirical Analysis on the role of model complexity](https://mlsanity.com/paper/2411.02184/) (2024)
- [The Price of Robustness: Stable Classifiers Need Overparameterization](https://mlsanity.com/paper/2603.02806/) (2026)

## Abstract (arXiv)

In recent years, machine learning models have achieved success based on the independently and identically distributed assumption. However, this assumption can be easily violated in real-world applications, leading to the Out-of-Distribution (OOD) problem. Understanding how modern over-parameterized DNNs behave under non-trivial natural distributional shifts is essential, as current theoretical understanding is insufficient. Existing theoretical works often provide meaningless results for over-parameterized models in OOD scenarios or even contradict empirical findings. To this end, we are investigating the performance of the over-parameterized model in terms of OOD generalization under the general benign overfitting conditions. Our analysis focuses on a random feature model and examines non-trivial natural distributional shifts, where the benign overfitting estimators demonstrate a constant excess OOD loss, despite achieving zero excess in-distribution (ID) loss. We demonstrate that in this scenario, further increasing the model's parameterization can significantly reduce the OOD loss. Intuitively, the variance term of ID loss remains low due to orthogonality of long-tail features, meaning overfitting noise during training generally doesn't raise testing loss. However, in OOD cases, distributional shift increases the variance term. Thankfully, the inherent shift is unrelated to individual x, maintaining the orthogonality of long-tail features. Expanding the hidden dimension can additionally improve this orthogonality by mapping the features into higher-dimensional spaces, thereby reducing the variance term. We further show that model ensembles also improve OOD loss, akin to increasing model capacity. These insights explain the empirical phenomenon of enhanced OOD generalization through model ensembles, supported by consistent simulations with theoretical results.