Does Your Optimizer Care How You Normalize? Normalization-Optimizer Coupling in LLM Training

• URL: http://arxiv.org/abs/2604.01563v1
• Date: Thu, 02 Apr 2026 03:20:58 GMT
• Title: Does Your Optimizer Care How You Normalize? Normalization-Optimizer Coupling in LLM Training
• Abstract summary: We show that Dynamic Erf (Derf) suffers a large negative interaction with Muon (Jordan, 2024)<n>Our evidence points to two failure modes of erf under Muon's faster spectral-norm growth: saturation (lossy compression) and scale blindness.<n>Using Derf's published default alpha with Muon incurs a 0.66-nat interaction penalty without producing NaNs or divergence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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