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Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs

ICLR 2021 · Architectures and efficiency › CNN design · approach: Theory of convolutional inductive bias · 81 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Train only BatchNorm γ and β, freezing the other weights at random initializationResNet-110 · CIFAR-10test accuracyHelped
Increase depth while training only BatchNorm γ and βResNet · CIFAR-10accuracy: 48% -> 82%Helped
Increase width while training only BatchNorm γ and βWRN · CIFAR-10accuracy: 48% -> 73%Helped
Increase depth while training only BatchNorm γ and βResNet · ImageNettop-5 accuracy: 17% -> 32%Helped
Train two random parameters per channel instead of the two BatchNorm affine parameters (ablation)ResNet · CIFAR-10accuracy: 17 to 21 percentage points lowerHurt
Train two random parameters per channel instead of the two BatchNorm affine parameters (ablation)ResNet · ImageNettop-5 accuracy: never exceeds 4%Hurt
Also train the output layer alongside BatchNorm (ablation)ResNet · ImageNettop-5 accuracy: about 25 percentage points; maximum value 57%Helped
Train the output layer alone, without BatchNorm (ablation)ResNet-200 · ImageNettop-5 accuracy: 2.7%Hurt
Initialize BatchNorm with β=1 instead of β=0 (ablation)BatchNorm-only ResNets · CIFAR-10 and ImageNetaccuracy: 1 to 3 percentage pointsHelped
Initialize BatchNorm with β=1 instead of β=0 (ablation)ResNet-200 with all parameters trainable · ImageNettop-5 accuracy: 0.5%Hurt
Initialize γ=1, β=0 or γ sampled from [-1, 1], β=0 (ablation)BatchNorm-only ResNets · CIFAR-10 and ImageNetaccuracyNo clear effect
Clamp BatchNorm γ values with |γ| < 0.01 to zero (ablation)ResNets · CIFAR-10 and ImageNetaccuracyNo clear effect

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