If you like this content and you are looking for similar, more polished Q & A’s, check out my new book Machine Learning Q and AI. log ( probas ), labels ) tensor ( 0.1446 ) binary_cross_entropy ( probas, labels ) tensor ( 0.1446 ) > labels = torch. log_softmax ( logits, dim = 1 ), labels ) tensor ( 2.4258 ) # BINARY CROSS ENTROPY VS MULTICLASS IMPLEMENTATION cross_entropy ( logits, labels ) tensor ( 2.4258 ) > torch. sigmoid ( logits ), labels ) tensor ( 0.3088 ) # MULTICLASS binary_cross_entropy_with_logits ( logits, labels ) tensor ( 0.3088 ) > torch. It just so happens that the derivative of the loss with respect to its input and the derivative of the log-softmax with respect to its input simplifies nicely (this is outlined in more detail in my lecture notes.) Note the main reason why PyTorch merges the log_softmax with the cross-entropy loss calculation in torch.nn.functional.cross_entropy is numerical stability. torch.nn.l_loss is like cross_entropy but takes log-probabilities (log-softmax) values as inputs.torch.nn.functional.cross_entropy takes logits as inputs (performs log_softmax internally).torch.nn.functional.binary_cross_entropy_with_logits takes logits as inputs.torch.nn.functional.binary_cross_entropy takes logistic sigmoid values as inputs.PyTorch Loss-Input Confusion (Cheatsheet) In PyTorch, these refer to implementations that accept different input arguments (but compute the same thing). PyTorch mixes and matches these terms, which in theory are interchangeable. Next, we specify the loss function as cross-entropy loss and the optimizer as Adam: The Adam optimizer is a robust, gradient-based optimization method. In short, cross-entropy is exactly the same as the negative log likelihood (these were two concepts that were originally developed independently in the field of computer science and statistics, and they are motivated differently, but it turns out that they compute excactly the same in our classification context.) ![]() Let’s understand the graph below which shows what influences hyperparameters \alpha and \gamma has on. Important point to note is when \gamma 0 0, Focal Loss becomes Cross-Entropy Loss. (This is similar to the multinomial logistic loss, also known as softmax regression.) The only difference between original Cross-Entropy Loss and Focal Loss are these hyperparameters: alpha ( \alpha ) and gamma ( \gamma ). Let $a$ be a placeholder variable for the logistic sigmoid function output:. ![]() (You can find more details in my lecture slides.) For related reasons, we minimize the negative log likelihood instead of maximizing the log likelihood. Maximizing likelihood is often reformulated as maximizing the log-likelihood, because taking the log allows us to replace the product over the features into a sum, which is numerically more stable/easier to optimize. Remember that we are usually interested in maximizing the likelihood of the correct class. The reasons why PyTorch implements different variants of the cross entropy loss are convenience and computational efficiency. Machine Learning FAQ Why are there so many ways to compute the Cross Entropy Loss in PyTorch and how do they differ?
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