Signed Rescue Routing: Harm-Aware Cascades for Efficient LLM Inference

Large language model (LLM) cascades reduce inference cost by routing easy queries to a small model and deferring hard queries to a larger one. Production cascades govern this deferral through a confidence threshold, but LLM confidence scores are miscalibrated, the threshold must be tuned per model pair and per domain, and no setting yields a formal bound on cascade accuracy. We introduce \textbf{Conformal Cascade} (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise. The procedure delivers a distribution-free, finite-sample accuracy guarantee. By a per-tier union bound, the prediction set at the accepting tier covers the correct answer with probability at least $1 - Kα$ for any user-specified $α$; under a selection-preservation condition (consistent with, but not strictly implied by, our marginal coverage results), the bound tightens to $1 - α$. We further characterise expected cascade cost as an explicit function of $α$ and the calibration-set acceptance rate. Across 18 multiple-choice benchmarks spanning science, medicine, commonsense, and standardized exams, evaluated on two-tier cascades drawn from four open-weight model families, CC strictly improves over the strongest calibration-tuned heuristic cascade on the majority of family--benchmark pairs, with the largest gains on reasoning-heavy benchmarks where majority vote is unreliable; on easier benchmarks the cascade commits the vast majority of queries to the small model at no accuracy cost. Extension to open-ended generation requires an answer-clustering step that we leave for future work. The method requires no model training and only black-box API access.

Efficient deployment of large language models (LLMs) in production forces a trade-off between accuracy and cost. Operators often default to a single model that is either expensive for easy queries or insufficient for hard ones. To address this challenge, we propose a two-stage cascaded solution. Stage 1 clusters incoming queries and assigns each cluster to its most cost-effective model. The cost budget for this routing process is set by an interpretable hyperparameter, tuned offline. Stage 2 adds a quality estimation (QE) cascade; when an output from Stage 1 is judged low-quality, the query is escalated to a stronger model. This ensures only hard or low-confidence cases reach the expensive models. On the test datasets, the cascaded system retains 97-99% of the strongest model's accuracy while reducing Time Per Output Token (TPOT). It requires only task-correctness labels and adapts to changes in the model pool without manual reconfiguration.

LLM cascades and model routing promise lower inference cost by sending easy queries to a small model and escalating hard ones to a large model, but most deployed routers use uncalibrated confidence scores and require per-workload threshold tuning. We present UCCI, a calibration-first router that maps token-level margin uncertainty to a per-query error probability via isotonic regression and selects the escalation threshold by constrained cost minimization. Under three explicit assumptions, threshold policies on the calibrated score are cost-optimal, and isotonic calibration achieves O(n^{-1/3}) sample complexity for expected calibration error (ECE). On a production named entity recognition workload of 75,000 queries served by 4B and 12B instruction-tuned LLMs on H100 GPUs, UCCI cuts inference cost by 31% (95% CI: [27%, 35%]) at micro-F1 = 0.91 while reducing ECE from 0.12 to 0.03. At the same operating point, UCCI beats entropy thresholding, split-conformal routing, and a FrugalGPT-style learned threshold. All cascade results use end-to-end routing on actual model outputs and measured H100 latency, not simulated routing from global accuracies or nominal API prices.