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Derivative of Softmax Cross-Entropy Loss with Respect to Logits
The derivative of the softmax cross-entropy loss with respect to any unnormalized logit reveals an elegant and intuitive result:
This derivative is exactly the difference between the conditional probability assigned to the class by the model's softmax operation and the actual observation recorded in the one-hot label vector . This elegant property is characteristic of any exponential family model and makes computing gradients for backpropagation extremely straightforward.
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A neural network's final layer produces the raw output scores (logits)
[2.0, 1.0, 0.1]for three possible classes. To convert these scores into class probabilities, a function is applied that first exponentiates each score and then normalizes these new values by dividing each by their sum. What is the resulting probability distribution? (Values are rounded to three decimal places).A function is used to convert a vector of raw, unnormalized scores
z = [z_1, z_2, ..., z_K]into a probability distribution. This function operates by first applying the standard exponential function to each score and then normalizing these new values by dividing each by their sum. If a constant valueCis added to every score in the input vectorz, resulting in a new vectorz' = [z_1+C, z_2+C, ..., z_K+C], how will the resulting output probability distribution be affected?Consider two input vectors of raw scores (logits) for a 3-class classification problem: Vector A =
[1, 2, 3]and Vector B =[1, 5, 10]. Both vectors are passed through a function that exponentiates each score and then normalizes the results by dividing by their sum. How will the resulting probability distribution for Vector B compare to the one for Vector A?Youâre reviewing an internal evaluation script tha...
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