TRIAGE: Reliability- and Load-Conditioned Escalation for Two-Tier LLM Serving with a Semantic Evidence Judge

Deciding when to escalate a query from a small language model to a larger one requires a cheap signal that predicts, before the large model is called, whether escalating would help. Semantic entropy, originally developed to detect hallucinations, is a natural candidate: it measures how much a model's sampled answers disagree in meaning, and high disagreement often signals an unreliable answer. We test it across three benchmarks and two model families. On GSM8K, with a small/large pair about twelve times apart in size, semantic entropy reliably distinguishes the small model's mistakes (AUROC 0.871) and improves routed accuracy over random escalation by up to nine points at matched cost. An earlier strong-looking result on a synthetic benchmark proved misleading: a simple rule based only on question difficulty, with no model involved, matched semantic entropy almost exactly. This paper's main contribution is a set of checks that catch this before it is reported as real. We show that scoring a cheap, question-only difficulty estimate alongside any signal reveals whether the signal adds real information or just tracks how hard a question looks; that two reasonable definitions of "escalation worked" can produce very different results on the same data; that a benchmark can leave almost no room for any signal to beat simply always using the large model; and that the true cost of live sampling can make routing more expensive than calling the large model directly. For a cheaper alternative that reuses cached past outcomes, we show how to predict whether it will work on a new dataset -- confirmed by correctly forecasting a collapse from AUROC 0.908 to chance level (0.518) ahead of time. We offer these as a general checklist for evaluating escalation signals.

Serving open-weight language models on premises forces a trade-off between accuracy and computational cost. Hosting models of different sizes lets easy queries go to a small, efficient model and hard ones to a large model. We present CRE-Router (Cluster, Route, Escalate), a two-stage method that decides which of these models answers each query. It clusters queries and routes each cluster to the model that best trades error against cost, under a budget on the time per output token (TPOT) or the end-to-end latency per request (E2EL). It then either accepts the answer or, when a quality estimator rejects it, escalates the query to the strong model. Routing decides before generation, so a hard query goes straight to the strong model; escalation decides after, so it can catch the errors routing cannot predict. It needs no annotation beyond task-correctness labels. We evaluate CRE-Router on TeleMath, TeleQnA and AIME, with pools of two to nine models served on A100 GPUs. CRE-Router is more accurate than the efficient models in its pool and comparable to the strong model it escalates to, at a lower cost per token. We also find that the choice of cost term decides which models serve the workload, that pricing each model per cluster shortens the wait per request, and that a change of hardware changes the best routing.

LLM cascades, in which a cheap model defers to an expensive one on low-confidence queries, are widely used to reduce inference cost. Given a pool of models, a practitioner must decide how many models to include and where to set each deferral threshold. We derive first-order optimality conditions showing that, at an optimum, the ratio of expected accuracy gain to expected downstream cost is equal across deferral boundaries. A local search based on these conditions closely matches exhaustive search. We also derive an identity that decomposes the accuracy gain of score-based escalation over random escalation into two AUROC terms. Across five benchmarks and nine deferral scores, with model sequences and thresholds optimized from a pool of eight models, two-model cascades improve mean test-set accuracy over single-model selection by 2.1 to 8.2 percentage points. However, allowing more than two models does not improve mean test-set accuracy in 118 of 135 comparisons across scorers, datasets, and depth caps, and adds at most 0.43 percentage points. To understand the role of deferral scores in depth gains, we conduct counterfactual experiments with simulated confidence scores. When these scores have high AUROC and reflect only whether the current model answered correctly, allowing more than two models improves test-set accuracy on four of five benchmarks. However, these gains do not persist when the scores also reflect query difficulty shared across models, even at the same AUROC. These results suggest that gains from additional depth depend on how well the confidence score separates correct from incorrect answers for the current model compared with later models.