From Sampled Outcomes to Capability Distributions: Rethinking Supervision for LLM Routing

Existing LLM routing methods often construct supervision from a single sampled response for each query--model pair. Because LLM generation is stochastic, however, such an observation can be an unstable estimate of model capability: semantically equivalent query formulations and repeated decoding may yield different scores and even different model preferences. We show that this instability can further propagate from routing labels to learned routing policies. To address this issue, we propose DARS (Distribution-Aware Routing Supervision), which estimates query-level model capability from repeated observations spanning semantics-preserving query rewrites and stochastic decoding. DARS summar...

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