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Solving Math Word Problems with Process-based and Outcome-based Feedback
Jonathan Uesato · Nate Kushman · Ramana Kumar · H. Francis Song · Noah Siegel · Lisa Wang · Antonia Creswell · Geoffrey Irving · Irina Higgins

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in MATH-AI: Toward Human-Level Mathematical Reasoning »

Recent work has shown that prompting language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise the finetuning of such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% to 12.7% final-answer error and from 14.0% to 3.4% reasoning error among final-answer-correct solutions.

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Author Information

Jonathan Uesato (DeepMind)
Nate Kushman (DeepMind)
Ramana Kumar (DeepMind)
H. Francis Song (DeepMind)
Noah Siegel (DeepMind)
Lisa Wang (Google)
Antonia Creswell (Imperial College London)

Antonia Creswell is a Senior Research Scientist at DeepMind in the Cognition team. Her work focuses on the learning and integration of object representations in dynamic models. She completed her PhD on representation learning at Imperial College London in the department of Bioengineering.

Geoffrey Irving (Google)
Irina Higgins (DeepMind)

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