Reliable Neural Collapse Approximation for Open-World Test-Time Adaptation

Traditional Test-Time Adaptation (TTA) methods assume that source and target domains share the same label space. However, real-world target domains often experience label distribution shifts alongside data distribution shifts, introducing unseen Out-Of-Distribution (OOD) classes. This setting is known as Open-World Test-Time Adaptation (OWTTA). In this scenario, standard entropy minimization fails because OOD samples corrupt the model updates. Existing OWTTA methods often rely on fixed source prototypes to filter OOD samples, but these prototypes are frequently unavailable due to privacy concerns or fail to align with the target domain due to the domain gap.

This paper proposes Reliable Neural Collapse approximation (ReNC) to tackle OWTTA by leveraging neural collapse as a structural prior. Neural collapse describes the terminal geometry of well-trained neural networks, where class means and classifier weights align into a Simplex Equiangular Tight Frame. ReNC theoretically justifies that pre-trained classifier weights serve as source-domain prototypes. By measuring cosine similarity between target samples and these prototypes, ReNC learns an adaptive threshold to cluster and filter out OOD samples. For the remaining In-Distribution samples, the method employs a neural collapse approximation mechanism that updates both the model parameters and the prototypes simultaneously, encouraging target features to form a compact, well-structured geometry.

Extensive experiments on standard open-world benchmarks demonstrate that ReNC outperforms existing baselines under joint data and label distribution shifts. Empirical analysis confirms that ReNC successfully preserves neural collapse properties in the target domain, showing that structural priors from training can guide reliable online adaptation. This work offers a parameter-free, practical framework for robust deployment of deep models in unconstrained environments.