![]() ![]() The class_balances can be used to introduce different loss contributions per class, as they do in the Facebook paper. The focusing_parameter is \(\gamma\), which by default is 2 and should be defined as a layer parameter in the net prototxt. Where logprobs stores, per each element of the batch, the sum of the binary cross entropy per each class. focusing_parameter # The class balancing factor can be included in labels by using scaled real values instead of binary labels.ĭata_loss = np. focusing_parameter else : # Loss form for positive classes If labels = 0 : # Loss form for negative classes # We sum the loss per class for each element of the batch num, 1 ]) # Compute cross-entropy lossįor c in range ( len ( labels )): # For each class we compute the binary cross-entropy loss exp ( - scores )) # Compute sigmoid activations So when using this Loss, the formulation of Cross Entroypy Loss for binary problems is often used:ĭef forward ( self, bottom, top ): labels = bottom. It’s called Binary Cross-Entropy Loss because it sets up a binary classification problem between \(C’ = 2\) classes for every class in \(C\), as explained above. That’s why it is used for multi-label classification, were the insight of an element belonging to a certain class should not influence the decision for another class. 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. It is a Sigmoid activation plus a Cross-Entropy loss. ![]() The Caffe Python layer of this Softmax loss supporting a multi-label setup with real numbers labels is available here Binary Cross-Entropy LossĪlso called Sigmoid Cross-Entropy loss. We compute the mean gradients of all the batch to run the backpropagation. For the positive classes in \(M\) we subtract 1 to the corresponding probs value and use scale_factor to match the gradient expression. As the gradient for all the classes \(C\) except positive classes \(M\) is equal to probs, we assign probs values to delta. In the backward pass we need to compute the gradients of each element of the batch respect to each one of the classes scores \(s\). If labels != 0 : # If positive classĭelta = scale_factor * ( delta - 1 ) + ( 1 - scale_factor ) * delta bottom. diff # If the class label is 0, the gradient is equal to probs Backward pass: Gradients computationĭef backward ( self, top, propagate_down, bottom ): delta = self. We then save the data_loss to display it and the probs to use them in the backward pass. The batch loss will be the mean loss of the elements in the batch. 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 to introduce class balancing. Then we compute the loss for each image in the batch considering there might be more than one positive label. We first compute Softmax activations for each class and store them in probs. log ( probs ) * labels * scale_factor # We sum the loss per class for each element of the batchĭata_loss = np. count_nonzero ( labels )) for c in range ( len ( labels )): # For each class num, 1 ]) # Compute cross-entropy lossįor r in range ( bottom. sum ( exp_scores, axis = 1, keepdims = True ) logprobs = np. max ( scores, axis = 1, keepdims = True ) # Compute Softmax activationsĮxp_scores = np. It is used for multi-class classification.ĭef forward ( self, bottom, top ): labels = bottom. If we use this loss, we will train a CNN to output a probability over the \(C\) classes for each image. It is a Softmax activation plus a Cross-Entropy loss. Is limited to binary classification (between two classes).Īlso called Softmax Loss. Is limited to multi-class classification (does not support multiple labels). Caffe: Multinomial Logistic Loss Layer.The layers of Caffe, Pytorch and Tensorflow than use a Cross-Entropy loss without an embedded activation function are: Logistic Loss and Multinomial Logistic Loss are other names for Cross-Entropy loss. See next Binary Cross-Entropy Loss section for more details. That is the case when we split a Multi-Label classification problem in \(C\) binary classification problems. \(t_1\) and \(s_1\) are the groundtruth and the score for \(C_1\), and \(t_2 = 1 - t_1\) and \(s_2 = 1 - s_1\) are the groundtruth and the score for \(C_2\). Where it’s assumed that there are two classes: \(C_1\) and \(C_2\). ![]()
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