Don't Trust: Verify -- Grounding LLM Quantitative Reasoning with
  Autoformalization
Jin Peng Zhou Charles Staats Wenda Li Christian Szegedy Kilian Q. Weinberger Yuhuai Wu
Large language models (LLM), such as Google's Minerva and OpenAI's GPT
families, are becoming increasingly capable of solving mathematical
quantitative reasoning problems. However, they still make unjustified logical
and computational errors in their reasoning steps and answers. In this paper,
we leverage the fact that if the training corpus of LLMs contained sufficiently
many examples of formal mathematics (e.g. in Isabelle, a formal theorem proving
environment), they can be prompted to translate i.e. autoformalize informal
mathematical statements into formal Isabelle code -- which can be verified
automatically for internal consistency. This provides a mechanism to
automatically reject solutions whose formalized versions are inconsistent
within themselves or with the formalized problem statement. We evaluate our
method on GSM8K, MATH and MultiArith datasets and demonstrate that our approach
provides a consistently better heuristic than vanilla majority voting -- the
previously best method to identify correct answers, by more than 12% on GSM8K.
In our experiments it improves results consistently across all datasets and LLM
model sizes. The code can be found at https://github.com/jinpz/dtv.