Graph neural network

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A graph neural network is a neural network architecture that learns representations and predictions from graph-structured data.

A graph neural network learns low-dimensional representations from nodes, features, and their connections, then supports predictions over graph problems. section 11.7

A practical graph-learning pipeline proceeds as follows:

• Represent the problem with node features and an adjacency matrix. section 11.7
• Generate graph embeddings through GNN or GCN message passing. section 11.7
• Use multilayer perceptrons to predict probabilities for nodes or edges. section 11.7
• Search the probability-guided graph with beam search to obtain a feasible candidate. section 11.7

Solving a TSP instance

A pretrained model can process TSP data, select greedy decoding, run in evaluation mode, and use CUDA when available; Gurobi helps eliminate subtours. section 11.7

Figure 11.16 End-to-end pipeline for combinatorial optimization problems

Follow the end-to-end pipeline from graph encoding through embedding, prediction, and graph search. section 11.7

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Explains encoding, message passing, prediction, search, and learning objectives, while deferring training implementation details to substantial code and preprocessing.

Examples

Uses TSP, pretrained models, node and edge probabilities, Concorde solutions, beam search, and a Gurobi-assisted implementation.

What it assumes

Assumes graph-problem formulation with node features and adjacency matrices, while introducing embeddings and message-passing use.

What you can do after

Apply it via pretrained models to predict and search feasible TSP solutions.

How it connects

Connects graph embeddings, adjacency matrices, message passing, GCNs, MLPs, beam search, supervised learning, and reinforcement learning.

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Also explained in

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  Graph Neural Networks in ActionA graph neural network architecture specifies the layers, computations, and connectivity used by a graph neural network.
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  Financial AI in PracticeA neural network that learns from graph-structured data by aggregating information across connected nodes.
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  Knowledge Graphs and LLMs in ActionA graph neural network is a neural network architecture that learns representations by propagating information among nodes and edges of a graph.
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  Machine Learning Algorithms in DepthA graph neural network is a neural-network architecture that computes representations by propagating information over graph-structured data.

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Related concepts

• graph attention networkincludes · A graph attention network is a graph neural network that uses attention weights to aggregate information from neighboring nodes, allowing their contributions to differ.
• graphuses · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
• PyTorch Geometricused by · PyTorch Geometric is an open-source Python library that extends PyTorch with data structures and operators for graph and geometric machine learning.
• node classificationuses · Node classification is a graph-learning task that predicts one or more discrete category labels for individual nodes in a graph.
• link predictionuses · Link prediction is a graph-learning task that estimates whether a connection exists or may occur between nodes, often by scoring candidate links.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.