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Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Cayley SGD with momentum instead of SGD | WRN-28-10 · CIFAR10 | classification error (%): 3.89 -> 3.66 | Helped |
| use Cayley ADAM instead of ADAM | WRN-28-10 · CIFAR100 | classification error (%): 18.52 -> 18.10 | Helped |
| use the iterative Cayley method instead of the closed-form Cayley transform | Cayley SGD and Cayley ADAM · WRN-28-10, CIFAR10 | training time per epoch (s): 1071.5 -> 218.7; 1071.5 -> 224.4 | Helped |
| add momentum to the closed-form Cayley optimization (ablation) | WRN-28-10 · CIFAR10 | classification error (%): 3.80 -> 3.66 | Helped |
| add momentum to the closed-form Cayley optimization (ablation) | WRN-28-10 · CIFAR100 | classification error (%): 18.68 -> 18.26 | Helped |
| use iterative Cayley SGD instead of the closed-form Cayley transform | Full-uRNN, hidden size 116 · Pixel-by-pixel MNIST | time per iteration (s): 2.10 -> 1.42 | Helped |
| use iterative Cayley ADAM instead of the closed-form Cayley transform | Full-uRNN, hidden size 512 · Pixel-by-pixel MNIST | accuracy (%): 96.9 -> 96.9 | No clear effect |
| increase iterative Cayley steps from s=0 to s=2 (ablation) | Full-uRNN, hidden size 116 · unitarity check | unitarity error: 3.231e-3 -> 7.384e-6 | Helped |
| increase iterative Cayley steps from s=0 to s=2 (ablation) | Full-uRNN, hidden size 512 · unitarity check | unitarity error: 6.787e-3 -> 2.562e-5 | Helped |
| use s=2 iterative Cayley instead of the closed-form transform (ablation) | Full-uRNN, hidden size 116 · unitarity check | unitarity error: 8.273e-5 -> 7.384e-6 | Helped |
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