Graph Contrastive Pre-training for Effective Theorem Reasoning

TL;DR

This paper introduces NeuroTactic, a graph neural network-based pre-training approach using contrastive learning to enhance theorem representation, significantly improving tactic prediction accuracy in interactive theorem proving.

Contribution

NeuroTactic is the first to apply graph contrastive pre-training for theorem representation learning in tactic prediction tasks.

Findings

Achieves state-of-the-art results on CoqGym dataset.

Highlights the importance of theorem representation learning.

Demonstrates the effectiveness of graph contrastive pre-training.

Abstract

Interactive theorem proving is a challenging and tedious process, which requires non-trivial expertise and detailed low-level instructions (or tactics) from human experts. Tactic prediction is a natural way to automate this process. Existing methods show promising results on tactic prediction by learning a deep neural network (DNN) based model from proofs written by human experts. In this paper, we propose NeuroTactic, a novel extension with a special focus on improving the representation learning for theorem proving. NeuroTactic leverages graph neural networks (GNNs) to represent the theorems and premises, and applies graph contrastive learning for pre-training. We demonstrate that the representation learning of theorems is essential to predict tactics. Compared with other methods, NeuroTactic achieves state-of-the-art performance on the CoqGym dataset.