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(WrappedNormalis theoretically equivalent) - Posterior distribution (
--posterior):Normal(WrappedNormalis theoretically equivalent) - Decoder architecture (
--dec):Linear(MLP) (Wrappedis theoretically equivalent) - Encoder architecture (
--enc):Linear(MLP) (Wrappedis theoretically equivalent)
PVAE (--manifold PoincareBall):
- Curvature (
--c): 1.0 - Prior distribution (
--prior):WrappedNormalorRiemannianNormal - Posterior distribution (
--posterior):WrappedNormalorRiemannianNormal - 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):WrappedorMob
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