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CP-Router: An Uncertainty-Aware Router Between LLM and LRM

AAAI 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 2 citations (OpenAlex)

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Proposes CP-Router, a training-free, model-agnostic router that uses conformal prediction set sizes from an LLM's option probabilities to decide whether to answer with the LLM or escalate to an LRM, with the error rate chosen by a new Full and Binary Entropy (FBE) criterion.

Problem

LRMs often overthink simple MCQA prompts, wasting tokens and sometimes losing accuracy relative to LLMs, so a practical, training-free way to route prompts between an LLM and an LRM is needed.

Approach

Uses conformal prediction set size under the LLM's softmax over answer-option logits as an uncertainty proxy: singleton sets go to the LLM, larger sets go to the LRM. The CP error rate is auto-selected by maximizing FBE, a combination of entropy over set-size distribution and binary entropy of singleton vs non-singleton split.

Key results

• On the Llama pairing, CP-Router achieves the highest token utility on all 6 MCQA benchmarks; e.g., on College Math it exceeds LRM accuracy by 1.2% while reducing tokens (58.8 -> 60.0 accuracy).
• On GSM8K (open-ended, Llama pairing), CP-Router reaches 77.9% accuracy, trailing the LRM by 1.1% while saving reasoning tokens for 32.9% of questions.
• On GPQA with DeepSeek-V3/R1, CP-Router outperforms both standalone models and routes only 54.7% of prompts to R1.

Surprising findings

• On CN-Chemistry with the Qwen pairing, CP-Router surpasses the stronger LLM (82.9 vs 82.1), showing routing can exceed the better single model.

Limitations

• Evaluated mainly on MCQA; open-ended QA extension relies on generating top-4 candidate answers plus an 'Others' option.
• Calibration of alpha via FBE is done by grid search on the test set, and CP guarantees require exchangeability.
• Token savings are modest on harder benchmarks such as high school and college math.

Experimental setup

Datasets: MMLU-STEM STEM-MCQA GSM8K GPQA LogiQA CN-Chemistry

Benchmarks: MMLU-STEM elementary math MMLU-STEM high school math MMLU-STEM college math LogiQA GPQA STEM-MCQA CN-Chemistry GSM8K

Metrics: accuracy token reduction ratio token utility

Baselines: Random routing Top-1 probability routing Response entropy routing Dynathink Explicit self-awareness routing LLM only LRM only

Builds on: conformal prediction Dynathink DeepSeek-R1-Distill

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