# Weisfeiler-Lehman Embedding for Molecular Graph Neural Networks

arXiv: https://arxiv.org/abs/2006.06909 · HTML: https://mlsanity.com/paper/2006.06909/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 2 of 2)

- [Graph Neural Networks with Local Graph Parameters](https://mlsanity.com/paper/2106.06707/) (2021)
- [Boosting Heterogeneous Catalyst Discovery by Structurally Constrained Deep Learning Models](https://mlsanity.com/paper/2207.05013/) (2022)

## Abstract (arXiv)

A graph neural network (GNN) is a good choice for predicting the chemical properties of molecules. Compared with other deep networks, however, the current performance of a GNN is limited owing to the "curse of depth." Inspired by long-established feature engineering in the field of chemistry, we expanded an atom representation using Weisfeiler-Lehman (WL) embedding, which is designed to capture local atomic patterns dominating the chemical properties of a molecule. In terms of representability, we show WL embedding can replace the first two layers of ReLU GNN -- a normal embedding and a hidden GNN layer -- with a smaller weight norm. We then demonstrate that WL embedding consistently improves the empirical performance over multiple GNN architectures and several molecular graph datasets.