Research map / Optimization / Implicit bias and generalization
Batch Normalization Orthogonalizes Representations in Deep Random Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add successive batch-normalization layers to random linear updates | Deep random MLPs · Deep random MLP | expected orthogonality gap: 2 \left(1-\frac{2}{3}\alpha\right)^{\ell}+ \frac{3 n}{\alpha\sqrt{d}} | Helped |
| Add batch normalization across layers | Deep random MLPs · Deep random MLP | squared Wasserstein-2 distance to isotropic Gaussian: 4n \left(1-\frac{2}{3}\alpha\right)^{\ell}+ \frac{6 n^2}{\alpha\sqrt{d}} | Helped |
| Replace batch normalization with vanilla random linear layers (ablation) | Deep random networks · Deep random network | orthogonality of hidden representations | Hurt |
| Add SVD-based iterative orthogonalization at initialization | Vanilla MLP · CIFAR10 | training slowdown with depth | Helped |
| Add SVD-based iterative orthogonalization at initialization | Convolutional networks · CIFAR10 | training speed | Helped |
| Use ReLU activations instead of linear activations (ablation) | Batch-normalized MLP and convolutional network · CIFAR10 | orthogonality-gap stability across layers | No clear effect |
| Use sigmoid or tanh activations instead of linear activations (ablation) | Batch-normalized networks · Random networks | stability of representations across layers | No clear effect |
| Increase network depth in vanilla networks without orthogonalizing initialization (ablation) | Vanilla MLP · CIFAR10 | training loss after 30 epochs | Hurt |
| Train from initially aligned representations rather than initially orthogonal representations (ablation) | SGD-trained neural networks · CIFAR10 | optimization speed | Hurt |
Closest papers by meaning
- Understanding Batch Normalization (NeurIPS 2018 · similarity 0.90)
- Norm matters: efficient and accurate normalization schemes in deep networks (NeurIPS 2018 · similarity 0.90)
- Batch Normalization Biases Residual Blocks Towards the Identity Function in Deep Networks (NeurIPS 2020 · similarity 0.90)
- Demystifying Batch Normalization in ReLU Networks: Equivalent Convex Optimization Models and Implicit Regularization (ICLR 2022 · similarity 0.90)
- Towards Training Without Depth Limits: Batch Normalization Without Gradient Explosion (ICLR 2024 · similarity 0.89)
- Batch Normalization Is Blind to the First and Second Derivatives of the Loss (AAAI 2024 · similarity 0.88)
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