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Scalable One-Pass Optimisation of High-Dimensional Weight-Update Hyperparameters by Implicit Differentiation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| optimise weight decay and learning rate in one pass | the proposed hyperparameter optimiser · UCI Energy | test MSE (mean): 24 \pm\,2 -> 2.1 \pm\,0.1 | Helped |
| add momentum optimisation (ablation) | Ours WD+LR · UCI Energy | test MSE (mean): 2.1 \pm\,0.1 -> 0.96 \pm\,0.08 | Helped |
| add independent per-parameter learning rates (ablation) | Ours WD+LR+M · UCI Energy | test MSE (mean): 0.96 \pm\,0.08 -> 0.6 \pm\,0.2 | Helped |
| add independent per-parameter learning rates (ablation) | Ours WD+LR+M · UCI Power | test MSE (mean): 17.19 \pm\,0.01 -> 16.69 \pm\,0.03 | Helped |
| add independent per-parameter learning rates (ablation) | Ours WD+LR+M · Fashion-MNIST | test cross-entropy (mean): 0.369 \pm\,0.002 -> 0.398 \pm\,0.004 | Hurt |
| add independent per-parameter learning rates (ablation) | Ours WD+LR+M · CIFAR-10 | test cross-entropy (mean): 1.13 \pm\,0.02 -> 1.33 \pm\,0.05 | Hurt |
| optimise weight decay, learning rate, and momentum instead of weight decay and learning rate alone (ablation) | Ours WD+LR · Fashion-MNIST | test cross-entropy (mean): 0.373 \pm\,0.002 -> 0.369 \pm\,0.002 | Helped |
| optimise weight decay, learning rate, and momentum instead of weight decay and learning rate alone (ablation) | Ours WD+LR · Penn Treebank | test perplexity (mean): 360 \pm\,20 -> 270 \pm\,30 | Helped |
| optimise weight decay, learning rate, and momentum instead of weight decay and learning rate alone (ablation) | Ours WD+LR · Kin8nm | test MSE (mean): 8.1 \pm\,0.2 -> 8.1 \pm\,0.4 | No clear effect |
| replace approximate hypergradients with exact differentiation through optimisation | Ours WD+LR+M · Fashion-MNIST | test cross-entropy (mean): 0.369 \pm\,0.002 -> 0.386 \pm\,0.001 | Hurt |
| increase the look-back horizon to all training steps (ablation) | Diff-through-Opt · UCI datasets | test loss | No clear effect |
| increase the look-back distance (ablation) | Ours WD+LR+M · UCI Energy | median final test loss | Mixed |
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