Train on the States You Deploy: Closed-Loop Hard Routing

A 31M learned sparse-attention model with native perplexity $49$ reaches perplexity $291$ when deployed with the hard routes it was trained to produce. Soft-only training omits the hard deployment-state distribution; because deployed routes are generated layer by layer, that distribution is closed-loop. We introduce *Closed-Loop Hard Routing* (CLHR), which keeps a differentiable soft path for router learning while training the backbone on the hard trajectory induced by its own decisions. In an exact reproduction of a public 31M-parameter protocol, CLHR reduces closed-loop deployment excess from $1.782$ to $0.0035$ nats across three seeds, changing the hard/native perplexity ratio from $5.94\times$ to $1.0035\times$. With the configuration frozen, the reduction transfers to 300M models on WikiText-103 ($0.796\to 0.049$) and FineWeb-Edu ($0.513\to 0.027$); on LAMBADA, standard hardening reduces accuracy from $13.2$ to $3.7$, whereas CLHR changes it from $13.9$ to $12.9$. A matched causal ladder shows that hard exposure, open-loop replay, and shuffled routing do not suffice. Across the tested settings, successful soft-to-hard deployment requires task supervision on useful, self-induced hard states.