#openai #math #imo

This is an interview with Stanislas Polu, research engineer at OpenAI and first author of the paper "Formal Mathematics Statement Curriculum Learning".

Watch the paper review here: https://youtu.be/lvYVuOmUVs8

OUTLINE:

0:00 - Intro

2:00 - How do you explain the big public reaction?

4:00 - What's the history behind the paper?

6:15 - How does algorithmic formal math work?

13:10 - How does expert iteration replace self-play?

22:30 - How is the language model trained and used?

30:50 - Why is every model fine-tuned on the initial state?

33:05 - What if we want to prove something we don't know already?

40:35 - How can machines and humans work together?

43:40 - Aren't most produced statements useless?

46:20 - A deeper look at the experimental results

50:10 - What were the high and low points during the research?

54:25 - Where do we go from here?

Paper: https://arxiv.org/abs/2202.01344

miniF2F benchmark: https://github.com/openai/miniF2F

Follow Stan here: https://twitter.com/spolu

Abstract:

We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark, automatically solving multiple challenging problems drawn from high school olympiads.

Authors: Stanislas Polu, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Igor Babuschkin, Ilya Sutskever

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