# Projection Pursuit CPCANet for Domain Generalization

arXiv: https://arxiv.org/abs/2607.22117 · HTML: https://mlsanity.com/paper/2607.22117/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 58 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [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)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [SelfReg: Self-supervised Contrastive Regularization for Domain Generalization](https://mlsanity.com/paper/2104.09841/) (2021)
- [Adaptive Risk Minimization: Learning to Adapt to Domain Shift](https://mlsanity.com/paper/2007.02931/) (2020)
- [Ensemble of Averages: Improving Model Selection and Boosting Performance in Domain Generalization](https://mlsanity.com/paper/2110.10832/) (2021)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [Uncovering the Disentanglement Capability in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2212.08698/) (2022)
- [Sharpness-Aware Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2303.10353/) (2023)
- [Towards Principled Disentanglement for Domain Generalization](https://mlsanity.com/paper/2111.13839/) (2021)
- [Sparse Mixture-of-Experts are Domain Generalizable Learners](https://mlsanity.com/paper/2206.04046/) (2022)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Trivializations for Gradient-Based Optimization on Manifolds](https://mlsanity.com/paper/1909.09501/) (2019)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Invariant and Transportable Representations for Anti-Causal Domain Shifts](https://mlsanity.com/paper/2207.01603/) (2022)

## Abstract (arXiv)

Domain Generalization (DG) aims to learn representations robust to distribution shifts. Recent geometric alignment methods, such as CPCANet, extract domain-invariant structures through batch-wise Common Principal Component Analysis (CPCA). However, CPCANet suffers from rank-deficient covariance estimation due to the small-sample-size issue in mini-batch training. To address this limitation, we propose Projection Pursuit CPCANet (PP-CPCANet), a covariance-free framework that learns a global orthogonal basis on the Stiefel manifold and jointly optimizes it with network parameters via the Cayley transform. We further introduce a symmetry-breaking detached-median PP dispersion objective to extract common principal components (CPCs) with dense and robust optimization signals. Experiments on four DG benchmarks show that PP-CPCANet achieves SOTA performance while maintaining stable training.