So we need puro compute the gradient of CE Loss respect each CNN class punteggio mediante \(s\)

So we need puro compute the gradient of CE Loss respect each CNN class punteggio mediante \(s\)

So we need puro compute the gradient of CE Loss respect each CNN class punteggio mediante \(s\) 150 150 mahrukh

So we need puro compute the gradient of CE Loss respect each CNN class punteggio mediante \(s\)

Defined the loss, now we’ll have to compute its gradient respect onesto the output neurons of the CNN sopra order onesto backpropagate it through the net and optimize the defined loss function tuning the net parameters. The loss terms coming from the negative classes are niente. However, the loss gradient respect those negative classes is not cancelled, since the Softmax of the positive class also depends on the negative classes scores.

The gradient expression will be the same for all \(C\) except for the ground truth class \(C_p\), because the score of \(C_p\) (\(s_p\)) is in the nominator.

  • Caffe: SoftmaxWithLoss Layer. Is limited preciso multi-class classification.
  • Pytorch: CrossEntropyLoss. Is limited to multi-class classification.
  • TensorFlow: softmax_cross_entropy. Is limited esatto multi-class classification.

Mediante this Facebook rete informatica they claim that, despite being counter-intuitive, Categorical Cross-Entropy loss, or Softmax loss worked better than Binary Cross-Entropy loss sopra their multi-label classification problem.

> Skip this part if you are not interested sopra Facebook or me using Softmax Loss for multi-label classification, which is not norma.

When Softmax loss is used is a multi-label contesto, the gradients get per bit more complex, since the loss contains an element for each positive class. Consider \(M\) are the positive classes of a sample. The CE Loss with Softmax activations would be:

Where each \(s_p\) durante \(M\) is the CNN punteggio for each positive class. As durante Facebook paper, I introduce a scaling factor \(1/M\) puro make the loss invariant preciso the number of positive classes, which ple.

As Caffe Softmax with Loss layer nor Multinomial Logistic Loss Layer accept multi-label targets, I implemented my own PyCaffe Softmax loss layer, following the specifications of the Facebook paper. Caffe python layers let’s us easily customize the operations done per the forward and backward passes of the layer:

Forward pass: Loss computation

We first compute Softmax activations for each class and paravent them mediante probs. Then we compute the loss for each image sopra the batch considering there might be more than one positive label. We use an scale_factor (\(M\)) and we also multiply losses by the labels, which can be binary or real numbers, so they can be used for instance onesto introduce class balancing. The batch loss will be the mean loss of the elements con the batch. We then save the data_loss to display it and the probs preciso use them sopra the backward pass.

Backward pass: Gradients computation

Mediante the backward pass we need to compute the gradients of each element of the batch respect onesto each one of the classes scores \(s\). As the gradient for all the classes \(C\) except positive classes \(M\) is equal to probs, we assign probs values to sbocco. For the positive classes con \(M\) we subtract 1 preciso the corresponding probs value and use scale_factor onesto scontro the gradient expression. We compute the mean gradients of all the batch sicuro run the backpropagation.

Binary Ciclocampestre-Entropy Loss

Also called Sigmoid Ciclocampestre-Entropy loss. It is a Sigmoid activation plus a Ciclocampestre-Entropy loss. Unlike Softmax loss it is independent for each vector component (class), meaning that the loss computed for every CNN output vector component is not affected by other component values. That’s why it is used for multi-label classification, were the insight of an element belonging preciso a insecable class should not influence the decision for another class. It’s called Binary Ciclocampestre-Entropy Loss because it sets up per binary classification problem between \(C’ = 2\) classes for every class durante \(C\), as explained above. So when using this Loss, the formulation of Cross Entroypy Loss for binary problems is often used:


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