# Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling

arXiv: https://arxiv.org/abs/1911.06904 · HTML: https://mlsanity.com/paper/1911.06904/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2019.

## Built on by (most cited first, 20 of 20)

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- [Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networks](https://mlsanity.com/paper/2212.05200/) (2022)
- [Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformers](https://mlsanity.com/paper/2507.07808/) (2025)
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## Abstract (arXiv)

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting structure-aware neural methods to work with the underlying graph representations of logical expressions. While more effective than character and token-level approaches, graph-based methods have often made representational trade-offs that limited their ability to capture key structural properties of their inputs. In this work we propose a novel approach for embedding logical formulae that is designed to overcome the representational limitations of prior approaches. Our architecture works for logics of different expressivity; e.g., first-order and higher-order logic. We evaluate our approach on two standard datasets and show that the proposed architecture achieves state-of-the-art performance on both premise selection and proof step classification.