Weight decay and explicit weight-norm constraints improve optimizer performance in language model pretraining, yet a unified understanding of why such control helps and how much is needed remains incomplete. We analyze norm control in Muon over the entire training trajectory using the \emph{accumulated effective learning rate}, $C_T=\sum_{t<T}η_t/\|W_t\|_F$, where $η_t$ is the nominal learning rate and $η_t/\|W_t\|_F$ is the effective learning rate relative to the weight norm. For bounded update directions, accumulation over any training interval bounds relative weight displacement. We show that vanilla Muon can accumulate only logarithmically, potentially limiting exploration and helping explain its slower empirical progress, whereas MuonW and MuonH guarantee at least linear accumulation under the stated conditions. Going beyond bounded-norm control, we show that sufficiently slow norm growth guarantees faster accumulation than the logarithmic worst case, opening up less restrictive optimizer designs. Based on this insight, we propose MuonGS, which uses Gram--Schmidt (GS) projection to remove the radial component of each Muon update without fixing the weight norm. With bounded update directions and a constant nominal learning rate, we prove that the weight norm grows at most proportionally to $\sqrt{t}$ after $t$ steps. Consequently, MuonGS guarantees $C_T=Ω(\sqrt{T})$, with accumulation sustained even in later training. Further, for smooth scale-invariant objectives we establish its $O(T^{-1/2})$ stationarity guarantee. In pretraining experiments with 160M- and 400M-parameter dense models as well as a 135M active- and 1B total- parameter MoE model, MuonGS achieves lower validation perplexity than MuonH at long training horizons. In particular, for the dense model it achieves an estimated token-equivalent speedup up to about $15\%$ at matched validation loss to MuonH.
The development of Large Language Models (LLMs) has led to significant advances across a wide range of language tasks, while simultaneously raising growing concerns about unauthorized online data exploitation and privacy leakage. Unlearnable examples (UEs) emerge as a promising defense by injecting crafted perturbations into data such that models trained on them exhibit degraded utility. However, existing methods for text protection are primarily designed for classification tasks and discriminative language models, which limits their broad applicability (e.g., instruction following or reasoning) in LLMs. In this work, we propose **TextCloak**, an RL-driven data synthesis framework that safeguards textual data against unauthorized LLM fine-tuning. TextCloak employs a *UE generative policy* that transforms clean text into unlearnable examples while preserving semantic fidelity and linguistic naturalness. To optimize the policy, we introduce **GRPO-UE**, which simulates the attacker's LLM fine-tuning and rewards downstream degradation via group-relative policy optimization. This overall formulates a bi-level optimization loop, allowing the generator to discover effective protective patterns. Comprehensive experiments on six publicly available datasets and nine state-of-the-art LLMs demonstrate that TextCloak consistently impairs unauthorized LLM fine-tuning while maintaining text utility for legitimate use. Further analyses confirm its transferability and robustness across model architectures, training configurations, and adaptive attacks, highlighting its broad applicability as a practical defense for online content.