Research map / Probabilistic and scientific modeling / Variational and generative sampling
Variational autoencoders in the presence of low-dimensional data: landscape and implicit bias
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gradient flow with the simplified linear VAE loss | Linear VAE · Low-dimensional linear Gaussian data | decoder support | Helped |
| Train a nonlinear VAE from a random start | Nonlinear VAE · Nonlinear synthetic manifolds | manifold support recovery | Hurt |
| Fit a linear VAE to low-dimensional linear Gaussian data | Linear VAE · Linear synthetic Gaussian | normalized eigenvalue error: 0.44; 0.71; 0.49; 0.47; 0.30; 0.45; 0.42 | Hurt |
| Clip decoder variance at e^-4 (ablation) | Nonlinear VAE · Sigmoid and sphere synthetic data | manifold recovery: Sigmoid Mean Manifold Error: 0.09 -> 0.15; 0.13 -> 0.15; 0.23 -> 0.23; 0.24 -> 0.23; 0.18 -> 0.24; 0.28 -> 0.24; Sphere | Mixed |
| Clip decoder variance at e^-4 (ablation) | Nonlinear VAE on sigmoid synthetic data · Sigmoid synthetic | encoder variance zero-count correspondence to intrinsic dimension | Helped |
| Clip decoder variance at e^-4 (ablation) | Nonlinear VAE on sphere synthetic data · Sphere synthetic | encoder variance zero-count correspondence to intrinsic dimension | Hurt |
| Lower the clipping threshold from e^-4 toward e^-8 (ablation) | Nonlinear VAE · Sigmoid and sphere synthetic data | visual fit to the ground-truth manifold | Mixed |
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