Mathematical proofs can be mechanised using proof assistants to eliminate gaps and errors. However, mechanisation still requires intensive labour. To promote automation, it is essential to capture high-level human mathematical reasoning , which we address as the problem of generating suitable propositions . We build a non-synthetic dataset from the largest repository of mechanised proofs and propose a task on causal reasoning, where a model is required to fill in a missing intermediate proposition given a causal context . Our experiments (using various neural sequence-to-sequence models) reveal that while the task is challenging, neural models can indeed capture non-trivial mathematical reasoning. We further propose a hierarchical transformer model that outperforms the transformer baseline.
A well-defined benchmark is essential for measuring and accelerating research progress of machine learning models. In this paper, we present a benchmark for high-level mathematical reasoning and study the reasoning capabilities of neural sequence-to-sequence models . We build a non-synthetic dataset from the largest repository of proofs written by human experts in a theorem prover. The dataset has a broad coverage of undergraduate and research-level mathematical and computer science theorems. In our defined task, a model is required to fill in a missing intermediate proposition given surrounding proofs. This task provides a starting point for the long-term goal of having machines generate human-readable proofs automatically . Our experiments and analysis reveal that while the task is challenging, neural models can capture non-trivial mathematical reasoning. We further design a hierarchical transformer that outperforms the transformer baseline.
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Mathematical proofs can be mechanised using proof assistants to eliminate gaps and errors. However, mechanisation still requires intensive labour. To promote automation, it is essential to capture
A well-defined benchmark is essential for measuring and accelerating research progress of machine learning models. In this paper, we present a benchmark for
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human mathematical reasoning , which we address as the problem of generating suitable propositions
mathematical reasoning and study the reasoning capabilities of neural sequence-to-sequence models
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mechanised proofs and propose a task on causal reasoning, where
proofs written by human experts in a theorem prover. The dataset has a broad coverage of undergraduate and research-level mathematical and computer science theorems. In our defined task,
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a causal context
surrounding proofs. This task provides a starting point for the long-term goal of having machines generate human-readable proofs automatically
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(using various neural sequence-to-sequence models)
and analysis
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indeed
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propose
design
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model