Margin-stabilized stateful routing

Use this at a binary accept-or-reject gate, token-pruning gate, early-exit module, or sparse adaptive-compute router rather than in the dense backbone. Let x contain the token or request representation and a compact resource-state vector. Let u_phi(x,a) be an immediate-utility head, hat_lambda(x,a) be an EMA or learned price for consuming the resource, and V_psi be a continuation-value head. If the state transition T(x,a) is discrete, compute g_psi(x,a)=V_psi(T(x,a))-V_psi(x); for a continuous resource state z, use g_psi(x,a)=V_psi(x,T(z,a))-V_psi(x,z). Form s=u_phi-hat_lambda+g_psi and route only when s>=m. Train the task objective jointly with the margin loss max(0,m-s_accepted)+max(0,m+s_rejected), using pseudo-labels from a compute-budget or accuracy-constrained oracle if available. Estimate score separation from data as the fifth percentile of accepted scores minus the ninety-fifth percentile of rejected scores. Initialize m to one quarter of this separation, clip it to a small positive interval, and periodically recalibrate it. The paper supplies the degeneracy diagnosis and the requirement for positive threshold separation; the transition model, value head, and calibration rule are engineering approximations. First test on CIFAR-100 early exiting or a small Transformer token-pruning task. Compare a confidence-threshold gate, an unregularized utility-minus-price gate, and this margin gate at matched FLOPs. Measure accuracy, saved FLOPs, decision flip rate under additive logit noise, and flip rate after int8 quantization. Success is lower flip rate and higher accuracy at equal compute, with accepted and rejected score distributions separated instead of concentrated near zero.