GNN Applications

Graph Neural Networks (GNNs) have evolved from academic research into widespread industrial applications. This note surveys representative works applying GNNs to molecular science, recommender systems, knowledge graphs, traffic prediction, graph generation, and point cloud processing, showcasing the powerful generality of graph learning.

Learning path: GNN fundamentals (GCN/GraphSAGE/GAT) → Message passing paradigm → Domain-specific graph construction → Representative models → Industrial practice

Molecular Property Prediction and Drug Discovery

Molecular Graph Representation

Molecules inherently possess graph structure: atoms are nodes and chemical bonds are edges. Node features in molecular graphs typically include atom type, charge, hybridization state, etc.; edge features include bond type (single/double/triple/aromatic), bond length, etc.

Element	Graph representation	Example features
Atom	Node	Atomic number, charge, chirality, number of hydrogens
Chemical bond	Edge	Bond type, conjugation, ring membership
Molecule	Graph	Molecular weight, LogP, TPSA

MPNN (Message Passing Neural Network)

Gilmer et al. (2017) proposed the MPNN framework, unifying various GNNs under the message passing paradigm:

Message phase:

\[ \mathbf{m}_v^{(t+1)} = \sum_{u \in \mathcal{N}(v)} M_t(\mathbf{h}_v^{(t)}, \mathbf{h}_u^{(t)}, \mathbf{e}_{vu}) \]

Update phase:

\[ \mathbf{h}_v^{(t+1)} = U_t(\mathbf{h}_v^{(t)}, \mathbf{m}_v^{(t+1)}) \]

Readout phase (graph-level prediction):

\[ \hat{y} = R\left(\{\mathbf{h}_v^{(T)} \mid v \in G\}\right) \]

where \(M_t\) is the message function, \(U_t\) is the update function, and \(R\) is the readout function (e.g., sum pooling + MLP).

SchNet

SchNet (Schutt et al., 2017) is designed specifically for 3D molecules, directly processing atomic spatial coordinates:

Uses radial basis functions (RBF) of interatomic distances as edge features
Continuous-filter convolution: The filter is a continuous function of interatomic distance
Satisfies rotational and translational invariance
Widely used in molecular dynamics simulations and energy prediction

Applications in Drug Discovery

Task	Input	Output	Representative methods
Molecular property prediction	Molecular graph	Solubility, toxicity, etc.	MPNN, AttentiveFP
Virtual screening	Drug-target pairs	Binding affinity	GraphDTA
Molecular generation	Prior distribution	Novel molecular structures	JT-VAE, GraphAF
Drug-drug interaction	Drug pair graph	Interaction type	MHCADDI

Recommender Systems

PinSage

PinSage (Ying et al., 2018) is an industrial-scale GNN recommender system developed by Pinterest, operating on graphs with billions of nodes:

Core techniques:

Random walk sampling: Uses Personalized PageRank to rank neighbors by importance, selecting the most relevant ones
Producer-consumer architecture: CPU handles neighbor sampling and computation graph construction; GPU executes GNN forward/backward passes
Curriculum learning: Uses random negative samples in early training, then switches to hard negatives (nodes that are close in embedding space but are not positive samples)
MapReduce inference: Offline batch generation of all node embeddings

LightGCN

LightGCN (He et al., 2020) achieves excellent results in recommendation through a minimalist design:

\[ \mathbf{e}_u^{(l+1)} = \sum_{i \in \mathcal{N}(u)} \frac{1}{\sqrt{|\mathcal{N}(u)|}\sqrt{|\mathcal{N}(i)|}} \mathbf{e}_i^{(l)} \]

Key simplifications:

Removes feature transformation matrices: No \(W^{(l)}\) is used
Removes nonlinear activation functions: No \(\sigma(\cdot)\) is used
Weighted sum of multi-layer embeddings: The final embedding is a weighted average across layers

\[ \mathbf{e}_u = \sum_{l=0}^{L} \alpha_l \; \mathbf{e}_u^{(l)} \]

Method	Core idea	Graph type	Advantage
PinSage	GraphSAGE + random walk	Bipartite graph	Industrial-scale scalability
LightGCN	Simplified GCN	User-item bipartite graph	Simple, efficient, SOTA
NGCF	GCN + collaborative signal	User-item bipartite graph	Explicitly models high-order interactions
SR-GNN	GNN + session graph	Graph built from session sequences	Captures intra-session item relationships

Knowledge Graph Reasoning

R-GCN (Relational GCN)

Edges in knowledge graphs have multiple types (relations), which standard GCN cannot handle. R-GCN (Schlichtkrull et al., 2018) learns a different transformation matrix for each relation type:

\[ \mathbf{h}_v^{(l+1)} = \sigma\left(\sum_{r \in \mathcal{R}} \sum_{u \in \mathcal{N}_r(v)} \frac{1}{c_{v,r}} W_r^{(l)} \mathbf{h}_u^{(l)} + W_0^{(l)} \mathbf{h}_v^{(l)}\right) \]

where \(\mathcal{R}\) is the set of relation types, \(\mathcal{N}_r(v)\) is the set of neighbors of node \(v\) under relation \(r\), and \(c_{v,r}\) is a normalization constant.

Parameter explosion problem: When there are many relation types, the number of parameters becomes enormous. Solutions:

Basis decomposition: \(W_r = \sum_{b=1}^{B} a_{rb} V_b\), a linear combination of a small number of basis matrices
Block diagonal decomposition: Constrains \(W_r\) to be block diagonal

Typical Tasks

Task	Description	Evaluation metrics
Link prediction	Predict missing triples \((h, r, t)\)	MRR, Hits@K
Entity classification	Predict the type of an entity	Accuracy, F1
Relation prediction	Predict the relation type between two entities	Accuracy

Traffic Prediction

STGCN (Spatio-Temporal Graph Convolutional Network)

STGCN (Yu et al., 2018) is a pioneering work applying GNNs to traffic prediction, jointly modeling spatial dependencies and temporal dependencies:

Spatial dimension: Road networks are natural graph structures (intersections as nodes, roads as edges); graph convolution captures spatial correlations.

Temporal dimension: Uses 1D causal convolutions (rather than RNNs) to capture temporal dependencies, avoiding the efficiency issues of recurrent computation.

Architecture: ST-Conv Block = Temporal convolution → Spatial graph convolution → Temporal convolution

\[ \text{ST-Conv}(\mathbf{X}) = \Gamma_1 * \left(\Theta * \left(\Gamma_0 * \mathbf{X}\right)\right) \]

where \(\Gamma\) denotes temporal convolution, \(\Theta\) denotes graph convolution, and \(*\) denotes the convolution operation.

Traffic prediction method	Spatial modeling	Temporal modeling	Characteristics
STGCN	ChebNet graph convolution	1D causal convolution	Efficient, parallel computation
DCRNN	Diffusion convolution	GRU	Captures directed diffusion processes
Graph WaveNet	Adaptive adjacency matrix	Dilated causal convolution	No predefined graph structure needed
ASTGCN	Attention graph convolution	Attention-based temporal	Dynamic spatio-temporal attention

Graph Generation

GraphRNN

GraphRNN (You et al., 2018) formulates graph generation as a sequence generation problem:

Graph-level RNN: Generates nodes sequentially, outputting a state for each new node
Edge-level RNN: For each new node, generates edges connecting it to existing nodes

The advantage is autoregressive generation of graph structure, capable of modeling complex graph distributions.

DiGress

DiGress (Vignac et al., 2023) is a graph generation model based on discrete diffusion:

Defines a discrete noise process over node types and edge types
The forward process gradually "corrupts" the graph into a random graph
The reverse process learns to denoise, recovering the target graph from the random graph
Uses a Graph Transformer as the denoising network

Method	Generation paradigm	Advantage	Limitation
GraphRNN	Autoregressive	Flexible, handles arbitrary graph sizes	Order-dependent generation, slow
GraphVAE	VAE	One-shot generation	Limited to fixed graph sizes
DiGress	Discrete diffusion	High quality, order-independent	Computationally intensive
GDSS	Continuous diffusion (SDE)	Handles continuous attributes	Requires continuous relaxation

Point Cloud Processing

From Point Clouds to Graphs

Point clouds are collections of discrete points in 3D space, widely used in autonomous driving, robotics, and AR/VR. Common methods for converting point clouds to graphs:

k-nearest neighbor graph (k-NN Graph): Each point connects to its \(k\) nearest neighbors
Radius graph: Connects point pairs within distance \(r\)
Delaunay triangulation: Constructs a graph based on triangulation

DGCNN (Dynamic Graph CNN)

DGCNN (Wang et al., 2019) dynamically constructs a k-NN graph in feature space (not just coordinate space):

Rebuilds the graph at each layer based on current features (dynamic graph)
EdgeConv operation: Defines edge features as the difference between center point and neighbor

\[ \mathbf{h}_v^{(l)} = \max_{u \in \mathcal{N}(v)} \text{MLP}\left(\mathbf{h}_v^{(l-1)} \| (\mathbf{h}_u^{(l-1)} - \mathbf{h}_v^{(l-1)})\right) \]

PointNet++ and Its Relationship to Graphs

PointNet++ (Qi et al., 2017), while not an explicit GNN, follows a hierarchical sample-group-aggregate paradigm that closely parallels GraphSAGE:

Operation	PointNet++	GraphSAGE analogy
Sampling	Farthest Point Sampling (FPS)	Target node selection
Grouping	Ball query / k-NN	Neighbor sampling
Aggregation	PointNet (max pooling)	Aggregation function (Pool)

Method	Graph construction	Core innovation	Application scenario
PointNet	No graph structure (independent points)	Permutation-invariant set function	Classification, segmentation baseline
PointNet++	Hierarchical local regions	Multi-scale grouping	Non-uniform point clouds
DGCNN	Dynamic k-NN in feature space	Dynamic graph + EdgeConv	Shape classification, segmentation
Point Transformer	k-NN graph + attention	Vector attention	Large-scale point cloud segmentation

Summary and Outlook

GNN applications have permeated nearly every domain involving relational data. The core paradigm is: identify graph structure in the problem → design appropriate message passing mechanisms → optimize for the downstream task.

Trend	Description
Pre-trained GNNs	Pre-training on large-scale unlabeled graph data, transferring to downstream tasks
GNN + LLM	Combining large language models to process textual attributes on graphs
Equivariant GNNs	Preserving geometric symmetries (rotational/translational equivariance) for molecules and physics
Scalability	More efficient sampling and training strategies supporting graphs with tens of billions of edges
Heterogeneous graphs	Processing real-world graphs with multiple node and edge types

Graphs are everywhere. Mastering the core ideas and application paradigms of GNNs is an essential part of understanding modern AI systems.