# CopRoute: Dependence-Aware Conformal Routing for Language Models

arXiv: https://arxiv.org/abs/2610.13276 · HTML: https://mlsanity.com/paper/2610.13276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 58 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 30 of 42)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Large Language Model Routing with Benchmark Datasets](https://mlsanity.com/paper/2309.15789/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Language Model Cascades: Token-level uncertainty and beyond](https://mlsanity.com/paper/2404.10136/) (2024)
- [Language Model Cascades](https://mlsanity.com/paper/2207.10342/) (2022)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [A Unified Approach to Routing and Cascading for LLMs](https://mlsanity.com/paper/2410.10347/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [RouterEval: A Comprehensive Benchmark for Routing LLMs to Explore Model-level Scaling Up in LLMs](https://mlsanity.com/paper/2503.10657/) (2025)
- [Great Models Think Alike and this Undermines AI Oversight](https://mlsanity.com/paper/2502.04313/) (2025)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [Harnessing the Power of Multiple Minds: Lessons Learned from LLM Routing](https://mlsanity.com/paper/2405.00467/) (2024)
- [Cost-Effective Online Multi-LLM Selection with Versatile Reward Models](https://mlsanity.com/paper/2405.16587/) (2024)
- [LLM Bandit: Cost-Efficient LLM Generation via Preference-Conditioned Dynamic Routing](https://mlsanity.com/paper/2502.02743/) (2025)
- [Learning the Parameters of Determinantal Point Process Kernels](https://mlsanity.com/paper/1402.4862/) (2014)
- [Doing More with Less: A Survey on Routing Strategies for Resource Optimisation in Large Language Model-Based Systems](https://mlsanity.com/paper/2502.00409/) (2025)

## Abstract (arXiv)

Set-based language model routing aims to increase the coverage of the event where at least one model answers a query correctly while controlling the number of inference calls made. Existing risk-controlled routing policies bound the all-miss risk (the probability that every model in the selected set fails) by calibrating a single conformal threshold and applying it to a nested family of model sets. Because each model is scored in isolation, these policies ignore the dependence structure of model failures. Models that share training data or architecture tend to fail on the same queries, so two individually strong models can be jointly redundant while a weaker but complementary model covers the queries that the others miss. To account for this dependence, which existing risk-controlled policies ignore, we propose CopRoute, which orders models by how many new queries each one answers correctly beyond those already selected, decides per query how far down that order to go, and then picks the smallest cutoff that still meets the target risk. We show that CopRoute's ordering attains, on the design data, the best guarantee any efficient fixed-ordering algorithm can give for the average number of calls to the first correct model, and that a separate calibration step certifies the all-miss risk of the deployed sets. On RouterBench and RouterEval, CopRoute attains the fewest certified calls on nine of ten datasets at a target risk of 0.05 and on eight of ten at 0.10, making up to 79 percent fewer calls (median 24 percent) than the state-of-the-art risk-controlled policy at the same certified all-miss risk.