Neurosymbolic router learns DFA to route edge queries, improving small-model accuracy and efficiency
arXiv:2609.35833v1 proposes a neurosymbolic router that classifies incoming queries and dispatches them to the cheapest correct solver, learning a deterministic finite automaton (DFA) with the L* algorithm using a small language model as a membership oracle. On a Raspberry Pi 4B evaluated on 100 unseen prompts from DeepMind Mathematics, GSM8K, and RuleTaker, the learned router achieves 100% routing accuracy and 98.3% overall accuracy with a 512-token reasoning budget (93.3% on word problems), outperforming Program-of-Thought (72.0%) and a tool-calling agent (58.7%), while answering formatted queries in 1–11 ms and, in a 30-token configuration, running 8.8× faster and 2.8× more energy-efficient than Program-of-Thought.