Neural Message Passing for Quantum Chemistry

Neural Message Passing for Quantum Chemistry introduced the Message Passing Neural Network (MPNN) framework, unifying various graph neural network architectures under a single formalism. It achieved state-of-the-art results on molecular property prediction.

The Problem

Molecules are naturally graphs: atoms are nodes, bonds are edges. Predicting properties like energy or toxicity requires learning from this graph structure.

Message Passing Framework

MPNNs operate in two phases:

1. Message Passing Phase

For $T$ timesteps, each node collects messages from neighbors:

$$m_v^{t+1} = \sum_{u \in N(v)} M_t(h_v^t, h_u^t, e_{vu})$$

Then updates its hidden state:

$$h_v^{t+1} = U_t(h_v^t, m_v^{t+1})$$

2. Readout Phase

Aggregate node features into a graph-level prediction:

$$\hat{y} = R(\{h_v^T | v \in G\})$$

Interactive Demo

Watch messages flow through a molecular graph:

Neural Message Passing

Layer 1/3Run MPNN

Example: Formaldehyde (CH₂O) molecule

Phase: Message Collection

m_v = Σ_u∈N(v) M(h_u, h_v, e_uv)

M

Message Function

U

Update Function

R

Readout Function

Key Components

Component	Function	Common Choices
M (Message)	Computes edge messages	MLP, attention
U (Update)	Updates node states	GRU, LSTM
R (Readout)	Graph-level output	Sum, attention

Unifying Prior Work

The MPNN framework encompasses:

• Convolutional Networks on Graphs (Duvenaud et al.)
• Gated Graph Neural Networks (Li et al.)
• Interaction Networks (Battaglia et al.)
• Deep Tensor Neural Networks (Schütt et al.)

Each is an MPNN with specific $M$, $U$, and $R$ functions.

Virtual Graph Elements

The paper introduced “virtual edges” connecting all atom pairs:

$$e_{vu} = (d_{vu}, \text{bond type})$$

where $d_{vu}$ is the 3D distance. This allows the network to reason about non-bonded interactions.

Results on QM9

Predicting molecular properties on the QM9 dataset:

Property	Units	MPNN Error
HOMO	eV	0.043
LUMO	eV	0.038
Gap	eV	0.066
μ	Debye	0.030

MPNN achieved chemical accuracy on most targets.

Why This Matters

1. Unified framework: Clarified the design space of graph neural networks
2. Practical impact: Enabled ML-accelerated drug discovery
3. Architectural insight: Showed that message passing is the key inductive bias

Legacy

MPNNs became the foundation for:

• SchNet — Continuous-filter convolutions
• DimeNet — Directional message passing
• Equivariant GNNs — Respecting 3D symmetries

Key Paper

• Neural Message Passing for Quantum Chemistry — Gilmer et al. (2017)
  https://arxiv.org/abs/1704.01212