Mathematical Reasoning via Self-supervised Skip-tree Training
This work addresses the challenge of improving AI's capability in formal mathematical reasoning, which is incremental as it builds on existing self-supervised methods with a new training task.
The paper tackled the problem of enabling logical reasoning in language models by applying self-supervised training to mathematical formulas, and found that models trained on a novel skip-tree task outperformed those on standard skip-sequence tasks in mathematical reasoning abilities.
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical statements, such as type inference, suggesting missing assumptions and completing equalities. To train language models for formal mathematics, we propose a novel skip-tree task. We find that models trained on the skip-tree task show surprisingly strong mathematical reasoning abilities, and outperform models trained on standard skip-sequence tasks. We also analyze the models' ability to formulate new conjectures by measuring how often the predictions are provable and useful in other proofs.