DuaShepherd: Integrating Stepwise Correctness and Potential Rewards for Mathematical Reasoning

TL;DR

DuaShepherd introduces a reward modeling framework that combines correctness and potential signals to improve mathematical reasoning in Large Language Models, achieving state-of-the-art results.

Contribution

It presents a novel multi-task reward model integrating correctness and potential signals, enhancing LLMs' mathematical reasoning capabilities.

Findings

Outperforms models trained on single signals

Achieves state-of-the-art results on MATH500 and ProcessBench

Demonstrates benefits of combined reward signals

Abstract

In this paper, we propose DuaShepherd, a novel reward modeling framework that integrates two complementary reward signals, correctness and potential, to enhance the mathematical reasoning capabilities of Large Language Models (LLMs). While correctness-based signals emphasize identification of stepwise errors, potential-based signals focus on the likelihood of reaching the correct final answer. We developed an automated pipeline for constructing large-scale reward modeling dataset with both signals. A unified, multi-head architecture was explored to train the two reward models in a multi-task setup, demonstrating benefits from learning both correctness and potential in parallel. By combining these two signals into a compound probability, our model achieves consistent performance improvements across multiple benchmarks. Empirical evaluations on MATH500 and ProcessBench confirm that this combined reward significantly outperforms models trained on either reward type alone, achieving state-of-the-art performance under comparable resource constraints.