Papers Notes_2_ VGG--Very Deep Convolutional Networks for Lage-scale Image Recognition

Architecture

input-224×224 RGB image
preprocess-subtract the mean RGB value,computed on the training set,from each pixel
stride-fixed to 1 pixel
padding-the spartial resolution is preserved after convolution, i.e. the padding is 1 pixel for 3×3 conv.
Max-pooling-performed over a 2×2 pixel window, with stride 2
All hidden layers are equipped with the rectification none-linearity(ReLU).
None contain Local Response Normalization(LRN)→do not improve the performance

1. 3×3 conv.
   a stack of two 3×3 conv. layers has an effective receptive field of 5×5
   three such layers have a 7×7 effective receptive field
   why a stack of three 3×3 conv. layers instead of a single 7×7 layer?
   ① incorporate three non-linear rectification layers instead of a single one→make the decision function more discriminative
   ② decrease the number of parameters
   three-layer 3×3 conv. stack with C channels, parameters→$3(3^2{C}^2)=27C^2$
   a single 7×7 conv. layer, parameters→$7^2{C}^2=49C^2$
2. 1×1 conv.
   increase the non-linearity of decision function without affecting the receptive fields of the conv. layers→an additional non-linearity is introduced by rectification function

Training

1. details
   batch size-256
   momentum-0.9
   weight decay-0.0005
   dropout ratio-0.5, for the first two fully-connected layers
   learning rate-0.01, decreased by a factor of 10 when the validation set accuracy stopped improving. decreased 3 times, learning stopped after 370K iterations(74 epochs)
2. initialization
   began with training A, shallow enough to be trained with random initialization
   training deeper, initialised first four conv. layers and the last three fully-connected layers with the layers of net A
   random initialization→sample the weights from a normal distribution with the zero mean and 0.01 variance. biases initialised with 0
3. augment
   ① randomly crop from rescaled training images(one crop per image per SGD iteration)
   ② random horizontal flipping
   ③ random RGB colour shift(same with AlexNet)
4. rescale
   S: smallest side of an isotropically-rescaled training image
   two approaches for setting S
   ① fix S(256 or 384)→single-scale training
   ② randomly sample S from a certain range $[S_{min},S_{max}]$ (use [256,384])→multi-scale training

Testing

1. rescale
   Q: smallest side of an isotropically-rescaled image, not necessarily equal to the training scale S
   input image size different→FC covert to conv.
   first FC layer→7×7 conv. layer
   the last two FC layers→1×1 conv. layers
   why 7×7?
   padding makes sure that the spartial resolution is preserved after conv. layer
   then resolution reduces only because of maxpool, specifically, reduces half
   i.e. structure A has 5 maxpool layers→224/2^5=7, so the output of conv. stack is 7×7×512
   for the first FC layer, one channel corresponds to 49 weights→convert to conv. layer, use the same parameters, so the kernel size needs to be 7×7
   no FC layer→input image size does not need to be 224×224→apply to the whole(uncropped) image
   result→a class map, the number of channels equals to the number of classes, a variable spatial resolution dependent on the input image size
   spatially average(sum-pooled)→obtain a fixed-size vector of class scores for the image
2. augment
   rescale+horizontal flipping, average→the final scores

Conclusion

confirm the importance of depth in visual representations

References

Very Deep Convolutional Networks for Lage-scale Image Recognition