Research map / Optimization / Implicit bias and generalization
Combining Explicit and Implicit Regularization for Efficient Learning in Deep Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the nuclear-to-Frobenius norm ratio penalty | Depth 1 linear network trained with Adam · Rank 5 matrix completion | test error: 1.00 -> 4$\bm{e}\bf{\texttt{-}7}$ | Helped |
| Add the nuclear-to-Frobenius norm ratio penalty | Depth 1 linear network trained with Adam · Rank 5 matrix completion | effective rank: 79 -> 5 | Helped |
| Use the ratio penalty with Adam instead of gradient descent | Depth 1 linear network · Rank 5 matrix completion | test error: 0.81 -> 4$\bm{e}\bf{\texttt{-}7}$ | Helped |
| Replace the ratio penalty with the nuclear norm penalty (ablation) | Depth 1 linear network trained with Adam · Rank 5 matrix completion | test error: 4$\bm{e}\bf{\texttt{-}7}$ vs. 0.36 | Hurt |
| Replace the ratio penalty with Schatten 1/2:2/3 penalty (ablation) | Depth 1 linear network trained with Adam · Rank 5 matrix completion | test error: 4$\bm{e}\bf{\texttt{-}7}$ vs. 0.72 | Hurt |
| Increase depth from 1 to 3 while using Adam and ratio penalty (ablation) | Linear network · Rank 5 matrix completion | test error: 4$\bm{e}\bf{\texttt{-}7}$ -> 4$\bm{e}\bf{\texttt{-}7}$ | No clear effect |
| Add the ratio penalty | Depth 1 LNN trained with Adam · MovieLens100K 90:10 split | RMSE: 1.844 -> 0.915 | Helped |
| Add the ratio penalty | Depth 1 LNN trained with Adam · MovieLens100K 80:20 split | RMSE: 1.822 -> 0.921 | Helped |
| Add the ratio penalty | Depth 1 LNN trained with gradient descent · MovieLens100K 90:10 split | RMSE: 2.814 -> 2.808 | Helped |
| Add the ratio penalty | Depth 1 LNN trained with gradient descent · MovieLens100K 80:20 split | RMSE: 2.797 -> 2.821 | Hurt |
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