Compositional Conformal Risk Control for Multi-Stage LLM Cascades

Yuxia Sun, Jiahuang Wang, Haoting Liu, Zhiwei Huang, Tingrui Pei +1

Multi-stage large language model (LLM) cascades balance accuracy and inference cost, but reliable deployment also requires controlling error risk and identifying its sources across stages. We propose Compositional Conformal Risk Control (CompCRC), a risk-control framework for pre-specified multi-stage LLM cascades. We decompose the risk of accepting incorrect answers into additive stage-wise contributions over the full query population, linking local risk budgets to a system-level guarantee. CompCRC constructs and freezes candidate budget allocations and acceptance thresholds, selects one candidate on independent data, and certifies its stage-wise risk contributions on separate held-out data. Under conditional exchangeability, we establish a finite-sample guarantee: the marginal expected accepted-error risk of the complete deployment procedure does not exceed the global risk budget. At the reported comparison budget of $α=0.45$, all three stages of CompCRC pass their local checks on MMLU, GSM8K, and HellaSwag. Compared with Global-CRC, which passes system-level risk certification at the same budget, CompCRC reduces observed accepted-error risk by 1.33--2.00 percentage points,…