LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

Abstract

While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce's view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only the fundamental reasoning biases can be learned from these tasks. This defines a new pre-training methodology called "LIME" (Learning Inductive bias for Mathematical rEasoning). Models trained with LIME significantly outperform vanilla transformers on four very different large mathematical reasoning benchmarks. Unlike dominating the computation cost as traditional pre-training approaches, LIME requires only a small fraction of the computation cost of the typical downstream task. The code for generating LIME tasks is available at https://github.com/tonywu95/LIME.

Published as a conference paper at ICML 2021 (16 pages)

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Cited by in corpus (4)

• Measuring Mathematical Problem Solving With the MATH Dataset
• Pretrained Transformers as Universal Computation Engines
• NaturalProofs: Mathematical Theorem Proving in Natural Language
• Proof Artifact Co-training for Theorem Proving with Language Models