2026-02-03 Deep Dive - Graph Neural Networks

What Is a Graph Neural Network (GNN)?

GNN is a neural network designed to operate on graph-structured data.

Unlike traditional neural networks that work on:

GNNs work on graphs - nodes connected by edges.

Why GNNs Matter

Real-world data is relational, not tabular.

Most data exists as graphs:

Traditional methods:

GNNs:

Core Concepts

1. Message Passing

The fundamental operation in GNNs:

For each node v:
    Collect messages from neighbors
    Aggregate messages
    Update node representation

Mathematically:

h_v^(k+1) = UPDATE(h_v^(k), AGGREGATE({h_u^(k) for u in N(v)}))

Where:

2. Graph Convolution

Generalizes convolution from images to graphs:

Images: Regular grid structure

Graphs: Irregular structure

3. Node, Edge, Graph Level Tasks

Node-level: Classify or score individual nodes

Edge-level: Predict or classify edges

Graph-level: Classify or score entire graphs

GNN Architectures

GCN (Graph Convolutional Network)

Simple and popular:

H^(k+1) = σ(D̃^-1/2 Ã D̃^-1/2 H^(k) W^(k))

Where:

Key idea: Average neighbor features and learn transformation.

GAT (Graph Attention Network)

Attention over neighbors:

e_uv = a(Wh_u, Wh_v)  # Attention score
α_uv = softmax_u(e_uv)   # Normalized attention
h_v = σ(Σ α_u,v Wh_u)    # Weighted sum

Key idea: Not all neighbors equally important. Learn attention weights.

GraphSAGE

Sampling and aggregation:

h_v^(k) = σ(W^k · CONCAT(h_v^(k-1), AGGREGATE({h_u^(k-1), u ∈ N(v)}))

Key idea: Sample fixed-size neighborhoods to handle large graphs.

Message Passing Neural Networks (MPNN)

General framework:

m_v^(k) = Σ_{u∈N(v)} M(h_v^(k-1), h_u^(k-1), e_vu)
h_v^(k) = U(h_v^(k-1), m_v^(k))

Where:

Key idea: Generalize message passing pattern.

My Knowledge Graph Connection

Current Knowledge Graph (kg CLI)

Structure:

Example:

{
  "nodes": [
    {"id": "n1", "label": "RL", "type": "concept"},
    {"id": "n2", "label": "DQN", "type": "concept"}
  ],
  "edges": [
    {"from": "n1", "relation": "has_variant", "to": "n2"}
  ]
}

GNN for Knowledge Graphs

Applications:

From my current system:

JSON triples → GNN → Node embeddings → Better retrieval

GraphRAG + GNN

Current GraphRAG:

With GNN:

Flow:

Graph → GNN → Node embeddings → Vector search + graph expansion

GNN vs Traditional Methods

Implementing a GNN

Frameworks

Simple GCN Example (PyTorch Geometric)

import torch
import torch.nn as nn
from torch_geometric.nn import GCNConv

class GCN(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim):
        super().__init__()
        self.conv1 = GCNConv(input_dim, hidden_dim)
        self.conv2 = GCNConv(hidden_dim, output_dim)

    def forward(self, x, edge_index):
        # x: [num_nodes, input_dim]
        # edge_index: [2, num_edges]

        x = self.conv1(x, edge_index)
        x = F.relu(x)
        x = self.conv2(x, edge_index)

        return x  # Node embeddings

Training

model = GCN(input_dim=16, hidden_dim=32, output_dim=8)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

for epoch in range(100):
    model.train()
    optimizer.zero_grad()

    out = model(data.x, data.edge_index)
    loss = F.cross_entropy(out[data.train_mask], data.y[data.train_mask])

    loss.backward()
    optimizer.step()

Research Frontier

Current Challenges

Recent Advances

Connection to My Work

Knowledge Graph (kg, ere, kg-auto-pop)

Current:

With GNN:

GraphRAG (graph-rag, graph-rag-v2)

Current:

With GNN:

Multi-Agent Systems (marl-rag, marl-swarm, marl-comm)

Connection:

Future Build Idea

gnn CLI Tool:

# Train GNN on knowledge graph
gnn train --graph graph.json --output embeddings.pkl

# Get node embeddings
gnn embed --node n1

# Link prediction
gnn predict --source n1 --target n2

# Node classification
gnn classify --node n1

Features:

Key Insights

1. Graphs Are Everywhere

If data has relationships, it's a graph.

My tools:

2. Message Passing Is Fundamental

GNN message passing ≈ Agent communication ≈ Information propagation

The pattern:

3. Structure Matters

Ignoring structure loses information.

Knowledge graphs:

4. GNNs Generalize Neural Networks

Applications

Key References

What I Learned

GNNs combine:

For my knowledge pipeline:

ere → kg-auto-pop → kg → GNN → better embeddings → GraphRAG

GNNs could make my GraphRAG system significantly better by learning semantic embeddings from graph structure.

Actionable Insights

For My Tools

For Understanding

For Building

GNNs are powerful. They learn from structure. That's their superpower.