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Large-Margin Softmax Loss for Convolutional Neural Networks

ICML 2016 · Label-efficient and robust learning › Recognition and long-tail · approach: Loss design and classifier theory · 431 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
replace softmax loss with L-Softmax (m=2,3,4)CNN on MNIST · MNISTerror rate (%): 0.40 -> 0.32/0.31/0.31Helped
replace softmax loss with L-Softmax (m=2,3,4)CNN on CIFAR10 (no augmentation) · CIFAR10error rate (%): 9.05 -> 7.73/7.66/7.58Helped
replace softmax loss with L-Softmax (m=2,3,4)CNN on CIFAR10+ (with augmentation) · CIFAR10+error rate (%): 6.50 -> 6.01/5.94/5.92Helped
replace softmax loss with L-Softmax (m=2,3,4)CNN on CIFAR100 · CIFAR100error rate (%): 32.74 -> 29.95/29.87/29.53Helped
replace softmax loss with L-Softmax (m=2,3,4) trained on WebFaceCNN for LFW face verification · LFWverification accuracy (%): 96.53 -> 97.81/98.27/98.71Helped
increase margin m from 2 to 4 in L-Softmax (ablation)CNN on CIFAR100 · CIFAR100error rate (%): 29.95 -> 29.53Helped
increase margin m from 2 to 4 in L-Softmax (ablation)CNN on CIFAR10+ · CIFAR10+error rate (%): 6.01 -> 5.92Helped
increase margin m from 2 to 4 in L-Softmax (ablation)MNIST · MNISTerror rate (%): 0.32 -> 0.31No clear effect
replace softmax with hinge loss (ablation)CNN on CIFAR10 · CIFAR10error rate (%): 9.05 -> 9.91Hurt
add contrastive loss to softmax (ablation)CNN on LFW · LFWverification accuracy (%): 96.53 -> 97.31Helped

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