Dynamic Latent Routing

We investigate the temporal concatenation of sub-policies in Markov Decision Processes (MDP) with time-varying reward functions. We introduce General Dijkstra Search (GDS), and prove that it discovers optimal goal-reaching policies by concatenating sub-policies optimal for intermediate goals. Motivated by the ``search, select, update'' principle underlying GDS, we propose Dynamic Latent Routing (DLR), a language-model post-training method that jointly learns discrete latent codes, routing policies, and model parameters through dynamic search in a single training stage. In low-data fine-tuning settings, DLR matches or outperforms supervised fine-tuning across four datasets and six models, achieving a mean gain of $+6.6$ percentage points, while prior discrete-latent baselines consistently underperform SFT. Mechanistic analyses and targeted code ablations show that DLR learns structured routing behaviors with distinct causal roles. In six-digit arithmetic, a canonical mechanistic interpretability benchmark, DLR externalizes into discrete routing tokens algorithmic subtasks previously studied through activation and circuit analysis.