Zero-shot Mathematical Problem Solving via Generative Pre-trained Transformers

Abstract

Mathematics is an effective testbed for measuring the problem-solving ability of machine learning models. The current benchmark for deep learning-based solutions is grade school math problems: given a natural language description of a problem, the task is to analyse the problem, exploit heuristics generated from a very large set of solved examples, and then generate an answer. In this paper, a descendant of the third generation of Generative Pre-trained Transformer Networks (GPT-3) is used to develop a zero-shot learning approach, to solve this problem. The proposed approach shows that coding based problem-solving is more effective than the natural language reasoning based one. Specifically, the architectural solution is built upon OpenAI Codex, a descendant of GPT-3 for programming tasks, trained on public GitHub repositories, the world's largest source code hosting service. Experimental results clearly show the potential of the approach: by exploiting the Python as programming language, proposed pipeline achieves the 18.63% solve rate against the 6.82% of GPT-3. Finally, by using a fine-tuned verifier, the correctness of the answer can be ranked at runtime, and then improved by generating a predefined number of trials. With this approach, for 10 trials and an ideal verifier, the proposed pipeline achieves 54.20% solve rate.