Continual learning (CL) and model merging (MM) both aim to obtain a single model that performs well across multiple tasks, challenged respectively by catastrophic forgetting and weight-disentanglement error. In the literature, these difficulties are merely treated separately and mitigated through a variety of solutions, while the geometry induced by the base optimizer is treated as an implementation detail. In this work, we show that the two difficulties are in fact two instances of the same phenomenon: a parameter update useful for one task shifts the model's outputs on another. We formalize this shared phenomenon as \textit{task interference} and reduce it to a common layer-wise Frobenius inner product $\langle ΔW_\ell, J_\ell(x)\rangle_F$. This quantity, in turn, is utilized to expose the role of the optimizer. We theoretically derive an upper bound that isolates the spectral norm $\|ΔW_\ell\|_2$ as an optimizer-controllable factor of task interference, and a per-mode analysis shows that this bound tracks the dominant part of the empirical interference. Specifically, we then identify the recent Muon optimizer as a mechanism that regulates this factor by construction. Our work reveals that its elegant control on spectral norm tightens the interference bound for both CL and MM, positioning Muon as a principled optimizer-centric approach complementary to existing solutions. Our theoretcal analysis is well validated by experimental results. Replacing the AdamW optimizer with Muon improves accuracy by up to +5.02 points on the eight-task model-merging benchmark across three CLIP backbones. For continual learning, Muon also delivers uniformly positive gains across ten class-incremental protocols, three task-incremental protocols, and the 11-task MTIL benchmark.
Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter $λ$ grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds and remaining robust to super-weight removal. Near saturation, alignment and decay approach balance, explaining the transition from weight-scale growth to relaxation. These force dynamics directly govern the squared-norm component underlying $λ(t)$; the remaining RMS-to-Weibull reconstruction offset is measurable and decomposes into bridge and integration components, totaling approximately 5-6% in densely sampled regions. To extend the analysis to real models where optimizer moments are unavailable, we introduce a spline displacement method that recovers the alignment force from sparse checkpoints with approximately 92-94% accuracy, about twice the naive two-point baseline. We further observe that the peak value of $λ(t)$ varies with training-data coherence in our experiments, suggesting a data-dependent component of weight-scale growth that we leave to a controlled follow-up study. Code and data are available at https://github.com/tiexinding/NPM-Weibull-public.