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Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Clip Euclidean feature magnitude before the exponential map | Hyperbolic classifier · MNIST, CIFAR10, CIFAR100, and ImageNet | accuracy: 94.42±0.29 -> 99.08±0.31; 88.82±0.51 -> 94.76±0.44; 72.26±0.41 -> 75.88±0.38; 65.74 -> 68.45 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic ProtoNet · CUB few-shot classification | accuracy: 61.18±0.24 -> 64.66±0.24; 79.51±0.16 -> 81.76±0.15 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic ProtoNet · miniImageNet few-shot classification | accuracy: 51.88±0.20 -> 53.01±0.22; 72.63±0.16 -> 72.66±0.15 | Mixed |
| Clip Euclidean feature magnitude | Hyperbolic classifier · CIFAR10-trained OOD detection, mean over OOD datasets | AUROC: 89.53 -> 91.38 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic classifier · CIFAR10-trained OOD detection, mean over OOD datasets | FPR95: 49.56 -> 43.74 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic classifier · CIFAR100-trained OOD detection, mean over OOD datasets | FPR95: 73.05 -> 63.50 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic classifier · CIFAR100-trained OOD detection, mean over OOD datasets | AUROC: 82.74 -> 83.43 | Helped |
| Clip Euclidean feature magnitude | Hyperbolic classifier · CIFAR100-trained OOD detection, mean over OOD datasets | AUPR: 95.88 -> 95.72 | No clear effect |
| Clip Euclidean feature magnitude | Hyperbolic classifier · MNIST FGSM adversarial training at ε=0.05, attack ε=0.2 | accuracy: 46.57 ± 2.09 % -> 74.97 ± 1.02 % | Helped |
| Increase clipping radius r (ablation) | Clipped HNN · MNIST, CIFAR10, and CIFAR100 | accuracy | Hurt |
| Decrease clipping radius r too far (ablation) | Clipped HNN · CIFAR10 and CIFAR100 | accuracy | Hurt |
| Replace hard feature clipping with a norm regularization term (ablation) | Hyperbolic neural network · Image classification | accuracy | Hurt |
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