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Riemannian approach to batch normalization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | WRN-28-10 · CIFAR-10 | classification error rate: 3.89 -> 3.85 | Helped |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | WRN-28-10 · CIFAR-10 | classification error rate: 3.89 -> 3.78 | Helped |
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | WRN-40-10 · CIFAR-10 | classification error rate: 3.72 -> 3.72 | No clear effect |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | WRN-40-10 · CIFAR-10 | classification error rate: 3.72 -> 3.80 | Hurt |
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | VGG-11 · CIFAR-10 | classification error rate: 7.43 -> 7.14 | Helped |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | VGG-11 · CIFAR-10 | classification error rate: 7.43 -> 7.59 | Hurt |
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | WRN-28-10 · CIFAR-100 | classification error rate: 18.66 -> 18.19 | Helped |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | WRN-40-10 · CIFAR-100 | classification error rate: 18.39 -> 17.85 | Helped |
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | VGG-11 · CIFAR-100 | classification error rate: 29.25 -> 28.02 | Helped |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | VGG-11 · CIFAR-100 | classification error rate: 29.25 -> 28.05 | Helped |
| Use Riemannian Adam instead of Euclidean SGD for BN weight vectors | WRN-22-8 · SVHN | classification error rate: 1.64 -> 1.55 | Helped |
| Use Riemannian SGD instead of Euclidean SGD for BN weight vectors | WRN-16-8 · SVHN | classification error rate: 1.60 -> 1.69 | Hurt |
Closest papers by meaning
- Riemannian batch normalization for SPD neural networks (NeurIPS 2019 · similarity 0.92)
- Batch Normalization for Neural Networks on Complex Domains (ICML 2026 · similarity 0.91)
- A Lie Group Approach to Riemannian Batch Normalization (ICLR 2024 · similarity 0.89)
- Towards Training Without Depth Limits: Batch Normalization Without Gradient Explosion (ICLR 2024 · similarity 0.87)
- Batch Normalization Alleviates the Spectral Bias in Coordinate Networks (CVPR 2024 · similarity 0.86)
- Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry (CVPR 2025 · similarity 0.86)
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