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Graph Neural Networkand its application on Molecular Science
SEONGOK RYU
DEPARTMENT OF CHEMISTRY, KAIST
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Introduction to GNNs
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Convolutional Neural Network– Best solution for Vision Recognition
• Based on sampling theorem
• Works on regular grid
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Recurrent Neural Network– Best solution for Natural Language Processing
• Based on Markov process
• Suitable for finding relationship between elements in a sequence
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HOWEVER,- There are other types of data as well as image, sequence, …- Which have “irregular” data distribution
Social Graph(Facebook, Wikipedia)
3D Mesh Molecular Graph
All you need is GRAPH!
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Graph Representation
𝑮𝒓𝒂𝒑𝒉 = 𝑮(𝑿, 𝑨)
X : Node, Vertex
- Individual person in a social network
- Atoms in a molecule
Represent elements of a system
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Graph Representation
𝑮𝒓𝒂𝒑𝒉 = 𝑮(𝑿, 𝑨)
A : Adjacency matrix
- Edges of a graph
- Connectivity, Relationship
Represent relationship, interaction between elements of the system
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Graph Neural Networks- Utilizing graphs for input of the neural networks
https://tkipf.github.io/graph-convolutional-networks/
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Graph Neural Networks
- What can we do with GNNs?
https://tkipf.github.io/graph-convolutional-networks/
• Node classification
• Link prediction
• Node2Vec, Subgraph2Vec, Graph2Vec
• Learning physics law from data
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Graph Neural Networks
- Node state : Feature extracted from the Graph Neural Network
https://tkipf.github.io/graph-convolutional-networks/
CNNs learn features from convolution operations and classify the objects
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Graph Neural Networks
- Node states : Feature extracted from the Graph Neural Network
https://tkipf.github.io/graph-convolutional-networks/
Update ‘hidden node states’, in other words, learn node features
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Graph Neural Networks
- Node states : Feature extracted from the Graph Neural Network
https://www.experoinc.com/post/node-classification-by-graph-convolutional-network
Then, we can do classification, regression,
and other works based on updated hidden node states
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Graph Convolution Networkand beyond
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Convolution Neural Network
- Learning weight parameter for sampling points on a regular grid
What NN learns
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Convolution Neural Network
- Learning weight parameter for sampling points on a regular grid
What NN learns
𝑿𝒊(𝒍+𝟏)= 𝝈( 𝒋∈[𝒊−𝒌,𝒊+𝒌]𝑾𝒋
(𝒍)𝑿𝒋(𝒍)+ 𝒃𝒋(𝒍)
)
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Graph Convolution Network
- For Irregular representations? Like Graph structure!
𝑿𝒊(𝒍+𝟏)= 𝝈(
𝒋∈[𝑵(𝒊)]
𝑾𝒋(𝒍)𝑿𝒋(𝒍)+ 𝒃𝒋(𝒍))
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Graph Convolution Network
- For Irregular representations? Like Graph structure!
𝑿𝟐(𝒍+𝟏)= 𝝈(𝑿𝟏
𝒍𝑾 𝒍 + 𝑿𝟐
𝒍𝑾 𝒍 + 𝑿𝟑
𝒍𝑾 𝒍 + 𝑿𝟒
𝒍𝑾 𝒍 )
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Graph Convolution Network
- For Irregular representations? Like Graph structure!
𝑿𝒊(𝒍+𝟏)= 𝝈(𝑨𝑿 𝒍 𝑾 𝒍 )
A : adjacency matrix – connectivity matrix between nodes
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Graph Attention Network – beyond GCN
- Attention mechanism again
𝑿𝟐(𝒍+𝟏)
= 𝝈(𝑿𝟏𝒍𝑾 𝒍 + 𝑿𝟐
𝒍𝑾 𝒍 + 𝑿𝟑
𝒍𝑾 𝒍 + 𝑿𝟒
𝒍𝑾 𝒍 )
• It simply sum node states with same
weights
• However, the neighborhoods must be
considered with different importances.
• All we need is an attention, again!
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Graph Attention Network – beyond GCN
- Attention mechanism again
• It simply sum node states with same
weights
• However, the neighborhoods must be
considered with different importances.
• All we need is an attention, again!
𝑿𝒊(𝒍+𝟏)= 𝝈(
𝒋∈[𝑵𝑵(𝒊)]
𝜶𝒊𝒋𝑾𝒋(𝒍)𝑿𝒋(𝒍)+ 𝒃𝒋(𝒍)) 𝜶𝒊𝒋 = 𝒇(𝑿𝒊
𝒍𝑾 𝒍 , 𝑿𝒋
𝒍𝑾(𝒍))
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Applications on Molecular Science
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Molecules
- A set of atoms consists the molecule
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GCN and attention mechanism
- We treat “physical interaction between atoms”, which is central principle of molecular
science, using GCN and attention mechanism
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Our Neural Network for the molecular system
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Our Neural Network for the molecular system
Final Node states
The neural network recognize several functional groups differently
Learning solubility of molecules
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Our Neural Network for the molecular system
Final Node states
Learning photovoltaic efficiency (QM phenomena)
Interestingly, The NN also can differentiate nodes according to the quantum mechanical characteristics.
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Our Neural Network for the molecular system
Graph Features
Learning solubility of molecules
Similar molecules are located closely in the graph latent space
L2-norm
Ascending order
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Our Neural Network for the molecular system
- Molecules can be represented by graph structures.
- We can precisely predict molecular properties using graph convolution with attention
mechanism.
- The neural network can classify atoms (nodes) according to the chemistry knowledge.
- Also similar molecules are located closely in graph latent space.
- Not only prediction, but also interpretable results for molecular science
- We have devised generative models for de novo molecular design.