README.md

Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders

Code for reproducing the experiments in the paper:

@inproceedings{mathieu2019poincare,
  title={Continuous Hierarchical Representations with Poincar\'e Variational Auto-Encoders},
  author={Mathieu, Emile and Le Lan, Charline and Maddison, Chris J. and Tomioka, Ryota and Whye Teh, Yee},
  booktitle={Advances in Neural Information Processing Systems},
  year={2019}
}

Prerequisites

pip install -r -U requirements.txt or python3 setup.py install --user

Models

VAE (--manifold Euclidean):

• Prior distribution (--prior): Normal (WrappedNormal is theoretically equivalent)
• Posterior distribution (--posterior): Normal (WrappedNormal is theoretically equivalent)
• Decoder architecture (--dec): Linear (MLP) (Wrapped is theoretically equivalent)
• Encoder architecture (--enc): Linear (MLP) (Wrapped is theoretically equivalent)

PVAE (--manifold PoincareBall):

• Curvature (--c): 1.0
• Prior distribution (--prior): WrappedNormal or RiemannianNormal
• Posterior distribution (--posterior): WrappedNormal or RiemannianNormal
• Decoder architecture (--dec):
  • Linear (MLP)
  • Wrapped (logarithm map followed by MLP),
  • Geo (first layer is based on geodesic distance to hyperplanes, followed by MLP)
  • Mob (based on Hyperbolic feed-forward layers from Ganea et al (2018))
• Encoder architecture (--enc): Wrapped or Mob

Run experiments

Synthetic dataset

python3 pvae/main.py --model tree --manifold PoincareBall --latent-dim 2 --hidden-dim 200 --prior-std 1.7 --c 1.2 --data-size 50 --data-params 6 2 1 1 5 5 --dec Wrapped --enc Wrapped  --prior RiemannianNormal --posterior RiemannianNormal --epochs 1000 --save-freq 1000 --lr 1e-3 --batch-size 64 --iwae-samples 5000

MNIST dataset

python3 pvae/main.py --model mnist --manifold Euclidean             --latent-dim 2 --hidden-dim 600 --prior Normal        --posterior Normal        --dec Wrapped --enc Wrapped --lr 5e-4 --epochs 80 --save-freq 80 --batch-size 128 --iwae-samples 5000
python3 pvae/main.py --model mnist --manifold PoincareBall --c 0.7  --latent-dim 2 --hidden-dim 600 --prior WrappedNormal --posterior WrappedNormal --dec Geo     --enc Wrapped --lr 5e-4 --epochs 80 --save-freq 80 --batch-size 128 --iwae-samples 5000

Custom dataset via csv file (placed in /data, no header, integer labels on last column)

python3 pvae/main.py --model csv --data-param CSV_NAME --data-size NB_FEATURES