# Can Domain Generalization be Guaranteed in Small-Sample Learning?

arXiv: https://arxiv.org/abs/2609.39512 · HTML: https://mlsanity.com/paper/2609.39512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Domain Generalization via Conditional Invariant Representation](https://mlsanity.com/paper/1807.08479/) (2018)
- [Invariant Information Bottleneck for Domain Generalization](https://mlsanity.com/paper/2106.06333/) (2021)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Provable Domain Generalization via Invariant-Feature Subspace Recovery](https://mlsanity.com/paper/2201.12919/) (2022)
- [Causal Balancing for Domain Generalization](https://mlsanity.com/paper/2206.05263/) (2022)
- [Generalization Error Bounds for Multiclass Sparse Linear Classifiers](https://mlsanity.com/paper/2204.06264/) (2022)
- [Learning Optimal Features via Partial Invariance](https://mlsanity.com/paper/2301.12067/) (2023)
- [A Study on the Impact of Data Augmentation for Training Convolutional Neural Networks in the Presence of Noisy Labels](https://mlsanity.com/paper/2208.11176/) (2022)
- [Distribution Shift Is Key to Learning Invariant Prediction](https://mlsanity.com/paper/2601.12296/) (2026)

## Abstract (arXiv)

The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation and generalization. Structural Risk Minimization (SRM) has long been regarded as a principled solution under the classical i.i.d. assumption. However, domain generalization (DG) violates this assumption, leaving the theoretical role of SRM in DG largely unexplored. To bridge this gap, we establish the first theoretical guarantees for SRM in DG under mild assumptions. Specifically, based on the concept of stability, we derive learning consistency and generalization error bounds and prove that these bounds become tight when the hypotheses satisfy the stability condition. Building upon this, under a specific hypothesis space assumption, we establish stability, learning, and generalization bounds for SRM. We further discuss the applicability of these bounds to deep learning. This work establishes theoretical foundations for SRM under distribution shifts and sheds light on the design of robust DG algorithms in small-sample scenarios.