Research map / Probabilistic and scientific modeling / Variational and generative sampling
Mixed-curvature Variational Autoencoders
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use universal-curvature 2D components instead of a Euclidean VAE | VAE · BDP, latent dim 6, spherical covariance | LL: -56.28 -> -55.56 | Helped |
| Use universal-curvature components instead of a Euclidean VAE | VAE · MNIST, latent dim 6, spherical covariance | LL: -97.16 -> -97.12 | No clear effect |
| Use universal-curvature components instead of a Euclidean VAE | VAE · MNIST, latent dim 12, diagonal covariance | LL: -79.51 -> -79.61 | No clear effect |
| Use a single universal-curvature component rather than 2D universal-curvature components (ablation) | Universal VAE · BDP, latent dim 6, spherical covariance | LL: -55.56 -> -55.84 | Hurt |
| Use 2D components rather than one large component (ablation) | Learnable-curvature VAE · BDP, latent dim 6 | LL | Helped |
| Replace Wrapped Normal with von Mises-Fisher for an all-spherical VAE (ablation) | Spherical VAE · BDP and MNIST, latent dim 6, spherical covariance | LL: BDP: -55.81 -> -55.78; MNIST: -96.71 -> -97.03 | Hurt |
| Use von Mises-Fisher for the spherical component within a mixed product (ablation) | Euclidean-hyperbolic-spherical product VAE · BDP, latent dim 6, spherical covariance | LL: -55.92 -> -55.82 | Helped |
| Use Riemannian Normal rather than Wrapped Normal in a Poincaré component (ablation) | Poincaré VAE · MNIST, latent dim 6, spherical covariance | LL: -97.56 -> -92.54 | Helped |
| Learn curvature rather than fixing it in mixed-product VAEs (ablation) | Mixed-curvature VAE · MNIST, latent dim 6, diagonal covariance | LL: -97.37 -> -97.29 | Hurt |
| Use products of small components rather than a single large component (ablation) | Learnable-curvature VAE · MNIST, latent dim 6, diagonal covariance | LL | Mixed |
| Use non-Euclidean geometry rather than Euclidean geometry | VAE · CIFAR-10, latent dim 6, diagonal covariance | LL: -1896.19 -> -1888.23 | Helped |
| Use a single universal-curvature component rather than universal-curvature 2D components (ablation) | Universal VAE · MNIST, latent dim 6, diagonal covariance | LL: -97.06 -> -96.90 | Helped |
Closest papers by meaning
- A Geometric Perspective on Variational Autoencoders (NeurIPS 2022 · similarity 0.93)
- Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders (NeurIPS 2019 · similarity 0.92)
- Learning Flat Latent Manifolds with VAEs (ICML 2020 · similarity 0.89)
- Geometrically regularized autoencoders for non-Euclidean data (ICLR 2023 · similarity 0.89)
- Variational Autoencoders with Riemannian Brownian Motion Priors (ICML 2020 · similarity 0.89)
- Graph Geometry-Preserving Autoencoders (ICML 2024 · similarity 0.86)
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