Research map / Learning theory and algorithms / Matrix and tensor methods
Loss Landscapes of Regularized Linear Autoencoders
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add separate L2 penalties on the encoder and decoder | Linear autoencoder · Mean-centered data with distinct singular values | principal-direction recovery | Helped |
| Use unregularized reconstruction loss instead of separate encoder/decoder L2 penalties (ablation) | Linear autoencoder · Synthetic data | principal-direction recovery | Hurt |
| Penalize the encoder-decoder product instead of the two weight matrices separately (ablation) | Linear autoencoder · Synthetic data | principal-direction recovery | Helped |
| Penalize the encoder-decoder product instead of the two weight matrices separately (ablation) | Linear autoencoder · MNIST test set | principal-direction recovery | Hurt |
| Remove separate L2 penalties from the encoder and decoder (ablation) | Sum-loss linear autoencoder · Critical points | encoder-decoder transpose symmetry | Hurt |
| Increase the separate-weight regularization above a principal-direction eigenvalue (ablation) | Sum-loss linear autoencoder · Principal directions with eigenvalue at most lambda | retained information | Hurt |
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