What Must Expert Formation Preserve? Formation–Deployment Compatibility in Channel-Composed Two-Expert Models

Mixture-of-experts (MoE) systems often couple two distinct choices: how experts are formed during training and how the resulting experts are combined at inference. We separate these factors in a controlled channel-composed expert model and study how training-time formation affects effective post-training deployment. Matched formation interventions vary assignment information, exact mixing values, low-order statistics, online adaptation, reference dependence, and stochasticity; the resulting frozen checkpoints are then evaluated under multiple deployment rules. Across ESC-50, Speech Commands V2, FSD50K, CIFAR-100, and Tiny ImageNet, no single formation–deployment pair dominates. To test whether learned coefficient-to-channel correspondence matters beyond the coefficient values themselves, we perform a post-hoc exploratory assignment intervention that preserves the exact learned coefficient multiset while permuting only its correspondence with representation channels. The aligned assignment outperforms its permutation mean on ESC-50, Speech Commands, CIFAR-100, and Tiny ImageNet, but not on FSD50K. On ESC-50, the aligned-minus-permuted effect is $+2.901$ Robust-B points with a descriptive fold-level 95% interval $[2.363,3.438]$; the corresponding learned-channel versus learned-scalar difference is $+2.056$ points $[1.528,2.583]$. Thus channel-assignment sensitivity is itself regime dependent. For the studied linear head, every fixed channel-wise composition compiles exactly into a single affine classifier. A separate reference-free $$\begin{gathered} N \\ in \\ 2,4,8 \end{gathered}$$ stress test shows that increasing expert count can help or hurt, with no monotonic trend across task, formation, and deployment. Together, these results identify formation–deployment compatibility as a distinct design problem.