Generating graphs with Generative Adversarial Networks

Oct 20^th, 2022

BMI/CS 775 Computational Network Biology�Fall 2022

Anthony Gitter

https://compnetbiocourse.discovery.wisc.edu

• Representation learning on graphs
• Graph neural networks
• Graph transformers
• Generative graph models

Topics in this section

Goals for today

• Generative Adversarial Network appeal and definitions
• Likelihood-based versus implicated generative models
• Loss functions
• Generating graphs
• Generating biological and biochemical graphs
• MolGAN molecule generation
• Alternative approaches for larger graphs
• Challenges in training Generative Adversarial Networks

Graph generation task

• Given:
• Example graphs from a desired distribution
• Score for a graph (optional)
• Do:
• Sample new graphs from that same distribution
• Preferentially sample graphs with high scores (optional)

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• Challenges:
• How do we represent the distribution of graphs with certain properties?
• How do we efficiently sample from it?

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Biochemical graph generation task

• Given:
• Example druglike chemical graphs
• A scoring function for drug-related chemical properties

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• Do:
• Sample new graphs that represent druglike chemicals

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• Key idea:
• No longer score existing chemical libraries for drug-related properties
• Directly generate candidate chemicals to synthesize

Generating classic random graphs

• Lobster graph:
• Central path (backbone)
• All other vertices ≤ 2 edges from backbone
• Easy to parameterize distribution and sample from it
• Expected number of nodes in backbone
• Probability of adding a layer 1 edge
• Probability of adding a layer 2 edge

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Generating classic random graphs

• Erdős-Rényi graph:
• Choose each possible edge with uniform probability
• Two parameters
• Number of nodes
• Probability of adding edge
• Barabási–Albert graph:
• Preferentially add new nodes to high degree nodes
• Two parameters
• Number of nodes
• Number of edges per new node

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Likelihood-based generative models

Generative Adversarial Networks (GANS)

• Generative model with a clever training strategy
• No explicit likelihood required for generated objects
• Can be much more difficult to train than variational autoencoders
• Powerful data synthesis applications
• Goodfellow et al. 2014 arXiv:1406.2661

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GAN examples: CycleGAN

• Image-to-image translation

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• Zhu et al. ICCV 2017 and code

GAN examples: image inpainting

• Context encoders

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• Pathak et al. CVPR 2016 and code

GAN examples: living portraits

• Few-Shot Adversarial Learning of Realistic Neural Talking Head Models
• Zakharov et al. 2019 arXiv:1905.08233
• Video

How does a GAN work?

• Frame as a two player game
• G: generator
• D: discriminator
• G wants to generate samples that fool the discriminator
• D wants to accurately distinguish real from generated samples

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How does a GAN work?

• Initially G generates unrealistic samples, easy for D

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• After training, the samples start to improve

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• Eventually D is fooled by the realistic samples from G

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Images from https://developers.google.com/machine-learning/gan/gan_structure

GAN neural network architecture

• G and D can each be some form of neural network
• G samples noise, generates an object
• D classifies real and generated objects

Image from https://developers.google.com/machine-learning/gan/gan_structure

GAN loss functions

Top Hat question

MolGAN: generating druglike molecules

• Generate small molecules (chemicals) that resemble known drugs
• Extend GAN framework by incentivizing certain properties

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Image from De Cao and Kipf 2018 arXiv:1805.11973

Druglike small molecules

• QM9 dataset enumerated 133,885 organic compounds and calculated properties
• Heavy atoms: carbon (C), oxygen (O), nitrogen (N), fluorine (F)
• Universe of graphs to generate
• Only up to nine heavy atoms (nodes)
• Three types of edges: single, double, triple bonds
• Estimate properties with RDKit
• Druglikeness
• Solubility
• Synthetizability

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MolGAN generator

Image from De Cao and Kipf 2018 arXiv:1805.11973

MolGAN discriminator

Image from De Cao and Kipf 2018 arXiv:1805.11973

Edge types

Adjacency matrix

for each edge type

MolGAN reward function

• Graph regression
• Same strategy as discriminator but predict continuous value
• Differentiable approximation of reward function from RDKit
• Inspired by Reinforcement Learning

Image from De Cao and Kipf 2018 arXiv:1805.11973

Overall generator objective

Generator parameters

Hyperparameter

MolGAN evaluation

MolGAN evaluation

MolGAN struggles to generate unique molecules

Challenges with GANs

• Sensitive to hyperparameters
• Training may not converge
• Difficult to evaluate
• Vanishing gradients: discriminator is too good at rejecting generated samples
• Mode collapse: generator repeatedly produces the same or very similar samples

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• Can observe some of these challenges interactively
• Train GAN to generate 2D data
• https://poloclub.github.io/ganlab/

Wasserstein GAN

Alternative graph generation approaches

• Reinforcement learning to add/remove graph components
• Recurrently add graph components
• Graph Recurrent Attention Networks (Liao et al. 2019 arXiv:1910.00760)

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• Scales to up to 5,000 nodes

Conclusions

• GANs are flexible generative models
• Do not require explicit likelihood function
• Approach is difficult to reproduce with traditional graph models
• Amazing synthesis capabilities in many domains
• Drug and protein design
• Not widely used in gene/protein networks
• Many practical challenges in training and evaluation

What’s next in generative modeling?

What’s next in generative modeling?

• Diffusion models are quickly replacing GANs in many domains
• Image generation
• Text prompt to image
• Text prompt to video
• Image to image translation
• Applications for proteins and chemicals

What’s next in generative modeling?

“Computers fighting bacteria, sci fi, high resolution”

Image from Keras Stable Diffusion Colab notebook

Fun to generate images

Many ethical issues to consider