Predictive Spectral Calibration for Source-Free Test-Time Regression

Test-time adaptation (TTA) has been widely explored to prevent performance degradation when test data differ from the training distribution. However, fully leveraging the rich representations of large pretrained models with minimal parameter updates remains underexplored. In this paper, we propose Intrinsic Mixture of Spectral Experts (IMSE) that leverages the spectral experts inherently embedded in Vision Transformers. We decompose each linear layer via singular value decomposition (SVD) and adapt only the singular values, while keeping the singular vectors fixed. We further identify a key limitation of entropy minimization in TTA: it often induces feature collapse, causing the model to rely on domain-specific features rather than class-discriminative features. To address this, we propose a diversity maximization loss based on expert-input alignment, which encourages diverse utilization of spectral experts during adaptation. In the continual test-time adaptation (CTTA) scenario, beyond preserving pretrained knowledge, it is crucial to retain and reuse knowledge from previously observed domains. We introduce Domain-Aware Spectral Code Retrieval, which estimates input distributions to detect domain shifts, and retrieves adapted singular values for rapid adaptation. Consequently, our method achieves state-of-the-art performance on various distribution-shift benchmarks under the TTA setting. In CTTA and Gradual CTTA, it further improves accuracy by 3.4 percentage points (pp) and 2.4 pp, respectively, while requiring 385 times fewer trainable parameters. Our code is available at https://github.com/baek85/IMSE.

Test-Time Adaptation (TTA) enhances the robustness of models against distribution shifts but faces two critical challenges: error accumulation from noisy pseudo-labels and catastrophic forgetting of source knowledge. Uncertainty-based approaches designed to mitigate error accumulation often yield overconfident or computationally expensive estimates, while strategies intended to prevent forgetting via prototype replay rely on static representations that easily become misaligned as the model adapts. To address these issues, this paper proposes a novel framework, Distilling Image Prototype for Guided Test-Time Adaptation (DIPTTA). The core of the proposed approach is the introduction of a Distill Image Prototype (DIP), a compact set of synthetic images that serves as a dynamic and regenerative anchor of source knowledge. This prototype enables a dynamic feature replay mechanism that continuously generates feature prototypes aligned with the current state of the model, thus effectively preventing catastrophic forgetting. Furthermore, the DIP anchors a source-calibrated uncertainty estimation method, which provides a less biased measure of sample reliability by leveraging stable source knowledge, thereby robustly suppressing error accumulation. Extensive experiments on multiple benchmarks demonstrate that DIPTTA significantly outperforms state-of-the-art methods, particularly under severe domain shifts. The source code is available at https://github.com/LiwenWang919/DIPTTA.

Open-Set Test-Time Adaptation (OSTTA) operates on non-stationary target streams where covariate and semantic shifts coexist. Existing TTA methods often obtain adaptation signals by updating model parameters or maintaining mutable memories, which can be costly and vulnerable to unknown samples. We present TALOR, a lightweight, backward-free rectification module that uses the source linear head as a geometric anchor. The head-induced basis decomposes each normalized feature into high-gain principal coordinates and low-gain tail coordinates. TALOR estimates a soft-routed affine correction in the principal subspace, combining a regime-level principal bias with a tail-conditioned slope that captures sample-level tail-to-principal coupling. Using weighted ridge regression, it subtracts this drift estimate from the principal coordinates, reconstructs the feature and feeds it into the source head. On the ImageNet-C benchmark with six csOOD datasets, TALOR outperforms the next-best UniEnt by 2.2% H-score while running 2.5x faster and using only 12% of its GPU memory; as a post-correction plug-in, it further boosts COME to 68.4% H-score with only 2% additional memory overhead.