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Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a Poincaré latent space instead of a Euclidean latent space | VAE on branching diffusion data with σ₀=1.7 and c=1.2 · Branching diffusion test | negative test marginal likelihood: 57.0_{±0.2} -> 55.6_{±0.2} | Helped |
| Increase the prior distortion σ₀ from 1 to 1.7 (ablation) | P-VAE c=1.2 on branching diffusion data · Branching diffusion test | negative test marginal likelihood: 56.6_{±0.2} -> 55.6_{±0.2} | Helped |
| Use a Poincaré latent space rather than a Euclidean latent space | VAE on MNIST, latent dimension 2 · MNIST test, latent dim 2 | negative test marginal likelihood: 144.5_{±0.4} -> 142.5_{±0.4} | Helped |
| Use a Poincaré latent space rather than a Euclidean latent space | VAE on MNIST, latent dimension 5 · MNIST test, latent dim 5 | negative test marginal likelihood: 114.7_{±0.1} -> 114.1_{±0.2} | Helped |
| Use a Poincaré latent space rather than a Euclidean latent space | VAE on MNIST, latent dimension 10 · MNIST test, latent dim 10 | negative test marginal likelihood: 100.2_{±0.1} -> 99.7_{±0.1} | Helped |
| Use a Poincaré latent space rather than a Euclidean latent space | VAE on MNIST, latent dimension 20 · MNIST test, latent dim 20 | negative test marginal likelihood: 97.6_{±0.1} -> 97.0_{±0.1} | Helped |
| Use a Riemannian normal instead of a wrapped normal (ablation) | P-VAE on MNIST, latent dimension 2 · MNIST test, latent dim 2 | negative test marginal likelihood: 143.8_{±0.6} -> 142.5_{±0.4} | Helped |
| Use a Riemannian normal instead of a wrapped normal (ablation) | P-VAE on MNIST, latent dimension 5 · MNIST test, latent dim 5 | negative test marginal likelihood: 114.7_{±0.1} -> 114.1_{±0.2} | Mixed |
| Use a Riemannian normal instead of a wrapped normal (ablation) | P-VAE on MNIST, latent dimension 10 · MNIST test, latent dim 10 | negative test marginal likelihood: 100.0_{±0.1} -> 99.7_{±0.1} | Mixed |
| Use a Riemannian normal instead of a wrapped normal (ablation) | P-VAE on MNIST, latent dimension 20 · MNIST test, latent dim 20 | negative test marginal likelihood: 97.2_{±0.1} -> 97.0_{±0.1} | Helped |
| Add a logarithm-map preprocessing layer before the MLP decoder (ablation) | P-VAE with wrapped normal on MNIST · MNIST decoder ablation | test marginal log-likelihood | Helped |
| Add a gyroplane layer as the first decoder layer (ablation) | P-VAE with wrapped normal on MNIST · MNIST decoder ablation | test marginal log-likelihood | Helped |
Closest papers by meaning
- Mixed-curvature Variational Autoencoders (ICLR 2020 · similarity 0.92)
- A Geometric Perspective on Variational Autoencoders (NeurIPS 2022 · similarity 0.91)
- Variational Autoencoders with Riemannian Brownian Motion Priors (ICML 2020 · similarity 0.88)
- Variational autoencoders in the presence of low-dimensional data: landscape and implicit bias (ICLR 2022 · similarity 0.88)
- Hyperbolic VAE via Latent Gaussian Distributions (NeurIPS 2023 · similarity 0.88)
- Poincaré Embeddings for Learning Hierarchical Representations (NeurIPS 2017 · similarity 0.88)
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