Improve Mathematical Reasoning in Language Models by Automated Process
  Supervision
Authors: name: Liangchen Luo, name: Yinxiao Liu, name: Rosanne Liu, name: Samrat Phatale, name: Harsh Lara, name: Yunxuan Li, name: Lei Shu, name: Yun Zhu, name: Lei Meng, name: Jiao Sun, name: Abhinav Rastogi

Complex multi-step reasoning tasks, such as solving mathematical problems or
generating code, remain a significant hurdle for even the most advanced large
language models (LLMs). Verifying LLM outputs with an Outcome Reward Model
(ORM) is a standard inference-time technique aimed at enhancing the reasoning
performance of LLMs. However, this still proves insufficient for reasoning
tasks with a lengthy or multi-hop reasoning chain, where the intermediate
outcomes are neither properly rewarded nor penalized. Process supervision
addresses this limitation by assigning intermediate rewards during the
reasoning process. To date, the methods used to collect process supervision
data have relied on either human annotation or per-step Monte Carlo estimation,
both prohibitively expensive to scale, thus hindering the broad application of
this technique. In response to this challenge, we propose a novel
divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named
OmegaPRM for the efficient collection of high-quality process
supervision data. This algorithm swiftly identifies the first error in the
Chain of Thought (CoT) with binary search and balances the positive and
negative examples, thereby ensuring both efficiency and quality. As a result,
we are able to collect over 1.5 million process supervision annotations to
train a Process Reward Model (PRM). Utilizing this fully automated process
supervision alongside the weighted self-consistency algorithm, we have enhanced
the instruction tuned Gemini Pro model's math reasoning performance, achieving
a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from
the 51\% base model performance. Additionally, the entire process operates
without any human intervention, making our method both financially and
computationally cost-effective compared to existing methods.