Training a Mixture-of-Experts (MoE) model at long context or large batch size fails as soon as any one component's peak allocation exceeds device memory, so the target is every peak at once, not the average footprint. Four are left unbounded by the parallelism plans in common use, and each grows differently: expert dispatch with the routing matrix, the vocabulary projection with tokens times vocabulary, gradient checkpoint boundaries with depth times sequence length, and optimizer state with parameter count. Which one runs out first changes with the model, the context length, and the device co