Confidence-Calibrated Small-Large Language Model Collaboration for Cost-Efficient Reasoning

TL;DR

This paper introduces COREA, a cost-effective system that combines small and large language models for reasoning tasks, improving efficiency while maintaining accuracy through confidence calibration and reinforcement learning.

Contribution

The paper presents COREA, a novel cascade system that calibrates and leverages small language models with large models to reduce costs in reasoning tasks.

Findings

Reduces cost by over 20% on multiple datasets.

Improves small model confidence calibration.

Maintains high accuracy with minimal performance drop.

Abstract

Large language models (LLMs) demonstrate superior reasoning capabilities compared to small language models (SLMs), but incur substantially higher costs. We propose COllaborative REAsoner (COREA), a system that cascades an SLM with an LLM to achieve a balance between accuracy and cost in complex reasoning tasks. COREA first attempts to answer questions using the SLM, which outputs both an answer and a verbalized confidence score. Questions with confidence below a predefined threshold are deferred to the LLM for more accurate resolution. We introduce a reinforcement learning-based training algorithm that aligns the SLM's confidence through an additional confidence calibration reward. Extensive experiments demonstrate that our method jointly improves the SLM's reasoning ability and confidence calibration across diverse datasets and model backbones. Compared to using the LLM alone, COREA reduces cost by 21.5% and 16.8% on out-of-domain math and non-math datasets, respectively, with only an absolute pass@1 drop within 2%.