Disagreement-Guided Weak-to-Strong Routing

Small language models are increasingly deployed on edge devices and robotic systems to meet cost and latency constraints, yet their limited capabilities can make reliable deployment challenging. Stronger models can provide assistance when needed, but deciding when to route a weak-model response to a stronger model often relies on signals of response correctness. In open-ended and agentic tasks, however, obtaining such signals can require costly ground-truth supervision that is difficult to obtain at scale. We revisit the foundations of weak-to-strong routing and ask whether routing decisions can instead be guided by signals that do not require ground-truth supervision. We first characterize the optimal weak-to-strong routing policy, while allowing for multiple weak-model responses generated through local inference. Building on this characterization, we derive a principled approximation to the optimal routing based on model-to-model comparison. In particular, we introduce a notion of model disagreement that can be measured directly from model-generated responses, without ground-truth supervision. Importantly, the approximation becomes increasingly accurate as the strong model becomes a better proxy for the ground-truth distribution. Across agentic and single-turn tasks, our approach effectively navigates the trade-off between routing cost and response accuracy without ground-truth supervision. Moreover, even when ground-truth correctness signals are available for training, disagreement-based routing can outperform methods trained directly to predict correctness.