PAID: Pairwise Angular-Invariant Decomposition for Continual Test-Time Adaptation

TL;DR

This paper introduces PAID, a novel method for continual test-time adaptation that preserves the pairwise angular structure of pre-trained weights, leading to improved domain adaptation performance.

Contribution

It systematically analyzes geometric properties of pre-trained weights and proposes a prior-driven approach that maintains angular invariance during adaptation.

Findings

PAID outperforms recent SOTA methods on four CTTA benchmarks.

Preserving pairwise angular structure improves adaptation stability.

Decomposing weights into magnitude and direction enhances domain invariance.

Abstract

Continual Test-Time Adaptation (CTTA) aims to online adapt a pre-trained model to changing environments during inference. Most existing methods focus on exploiting target data, while overlooking another crucial source of information, the pre-trained weights, which encode underutilized domain-invariant priors. This paper takes the geometric attributes of pre-trained weights as a starting point, systematically analyzing three key components: magnitude, absolute angle, and pairwise angular structure. We find that the pairwise angular structure remains stable across diverse corrupted domains and encodes domain-invariant semantic information, suggesting it should be preserved during adaptation. Based on this insight, we propose PAID (Pairwise Angular-Invariant Decomposition), a prior-driven CTTA method that decomposes weight into magnitude and direction, and introduces a learnable orthogonal matrix via Householder reflections to globally rotate direction while preserving the pairwise angular structure. During adaptation, only the magnitudes and the orthogonal matrices are updated. PAID achieves consistent improvements over recent SOTA methods on four widely used CTTA benchmarks, demonstrating that preserving pairwise angular structure offers a simple yet effective principle for CTTA.