PyroDash Cuts a $49.36 Reasoning Run to $1.78 by Letting a Small Model Emit a Control Token When It Needs Help

arXiv 2607.20327·medium signal

Rather than a separate router, PyroDash internalizes the escalation policy inside the small model: mid-generation the SLM emits a control token, and a Collaborate Engine hands the query plus partial reasoning trace to a frozen LLM for a single completion — no LLM retraining and no logit access required. Trained in three stages ending with cost-aware GRPO, it exposes a tunable accuracy/cost frontier: at λ=0.05 it scores 64.04% average accuracy across five math benchmarks (6.36pp above LLM-only) at 20.4% lower cost; at λ=0.6 it holds 54.55% with a 1.90% LLM token ratio, dropping total cost from $49.36 to $1.78.