arXiv:2604.01563v1 Announce Type: new Abstract: In LLM training, normalization layers and optimizers are typically treated as independent design choices. In a 3x2 factorial at 1B parameters and 1000 training steps, we show this assumption can fail: Dynamic Erf (Derf; Chen & Liu, 2025) suffers a large negative interaction with Muon (Jordan, 2024), with its gap to RMSNorm growing from +0.31 nats under AdamW to +0.97 under Muon, approximately three times larger. Dynamic Tanh (DyT; Zhu et al., 2025), included as a bounded-normalizer control, shows no such penalty. Our evidence points to two failure modes of erf under Muon's faster spectral-norm growth: saturation (lossy compression) and scale blindness (discarding activation magnitude). An EMA-blend that reintroduces running scale estimates recovers ~84% of the gap. Separately, reducing Derf's alpha from its published default (0.5 to 0.3) recovers ~80% by keeping erf in its near-linear regime, where it approximately preserves relative scale; this setting is not the published default of Chen & Liu (2025). Using Derf's published default alpha with Muon incurs a 0.66-nat interaction penalty without producing NaNs or divergence, making the failure easy to miss in short pilot runs.

arXiv:2603.07926v1 Announce Type: cross Abstract: 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.