域泛化之投影追蹤CPCANet

摘要

域泛化（Domain Generalization, DG）旨在學習對分佈偏移具有穩健性的表徵。近期如CPCANet等幾何對齊方法，通過批次式共同主成分分析（Common Principal Component Analysis, CPCA）提取域不變結構。然而，CPCANet因小批量訓練中的小樣本量問題而面臨協方差估計秩不足的困境。為解決此限制，我們提出投影追蹤CPCANet（Projection Pursuit CPCANet, PP-CPCANet）——一種無需協方差的框架，可在斯蒂弗爾流形（Stiefel manifold）上學習全局正交基底，並透過凱萊變換（Cayley transform）將其與網絡參數聯合優化。我們進一步引入對稱性破缺的分離中位數PP離散度目標，以提取具有密集且穩健優化信號的共同主成分（CPCs）。在四個域泛化基準測試上的實驗顯示，PP-CPCANet在實現最先進性能的同時，保持了穩定的訓練過程。

English

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.