# Questions tagged [cross-entropy]

For questions related to the concept of cross-entropy in the context of artificial intelligence. For example, when the cross-entropy is used as a loss function to train a neural network.

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### Deriving the cross entropy loss via maximum-likelihood estimation?

For multi-class classification problems, we use the cross entropy loss, which can be derived from a multinomial distribution via the maximum likelihoos estimation method. I've already tried to derive ...
1 vote
33 views

### Trouble writing the backpropagation algorithm in python through crossentropy and softmax

so I am writing my own neural network library for a class project and I got everything working for a simple 2-class test using the distance (L2) cost function. I wanted to get a similar result using ...
319 views

### Focal Loss vs Weighted Cross Entropy Loss

Weighted Focal Loss is defined like so $FL(p_t) = -\alpha_t log(p_t) (1-p_t)^\gamma$ Whereas weighted Cross Entropy Loss is defined like so $CE(p_t) = -\alpha_t log(p_t)$ Some blog posts try to ...
88 views

### Why is the cross-entropy a cost function?

The question looks foolish, but I think cross-entropy is somewhat weird as a cost function. As a cost function for linear regression, the mean square error $\sum_{i=1}^{n} (y_i - (ax_i+b)) ^2$ seems ...
39 views

### Is categorical cross entropy better than binary cross entropy for imbalanced binary classification problems

I am training a NN model. The data is highly imbalanced (3% for positive labels), and I have not resampled more true classes in the training set. The model performs much better when categorical cross-...
126 views

For a multitask learning model, I've seen that approaches usually mask the output that doesn't have a label with zeros. As an example, have a look here: How to Multi-task learning with missing labels ...
1k views

206 views

### Where is the mistake in my derivation of the GAN loss function?

I was pondering on the loss function of GAN, and the following thing turned out \begin{aligned} L(D, G) & = \mathbb{E}_{x \sim p_{r}(x)} [\log D(x)] + \mathbb{E}_{x \sim p_g(x)} [\log(1 - D(x)] \...
209 views

### How does the implementation of the VAE's objective function equate to ELBO?

For a lot of VAE implementations I've seen in code, it's not really obvious to me how it equates to ELBO. $$L(X)=H(Q)-H(Q:P(X,Z))=\sum_ZQ(Z)logP(Z,X)-\sum_ZQ(Z)log(Q(Z))$$ The above is the definition ...
1 vote
203 views

1 vote
62 views

### Are sentences from the same document independent and identically distributed?

I am trying to build an LSTM model to generate Shakspeare-like poems. I have data set $\{s_1, s_2, \dots, s_m \}$, which are sentences of Shakespeare poems, and each sentence contains words \$\{w_1, ...
55 views

### How should I penalize the model proportionally to the error?

I am making an MNIST classifier. I am using categorical cross-entropy as my loss function. I want to make it so that if the correct label is 3, then it will penalize the model less heavily if it ...
1 vote
78 views

### Why does PyTorch use a different formula for the cross-entropy?

In my understanding, the formula to calculate the cross-entropy is $$H(p,q) = - \sum p_i \log(q_i)$$ But in PyTorch nn.CrossEntropyLoss is calculated using this ...
111 views

### How to formalize learning in terms of information theory?

Consider the following game on a MNIST dataset: There are 60000 images. You can pick any 1000 images and train your Neural Network without access to the rest of images. Your final result is ...
382 views

### Why does the binary cross-entropy work better than categorical cross-entropy in a multi-class single label problem?

I was just doing a simple NN example with the fashion MNIST dataset, where I was getting 97% accuracy, when I noticed that I was using Binary cross-entropy instead of categorical cross-entropy by ...
7k views

### How is division by zero avoided when implementing back-propagation for a neural network with sigmoid at the output neuron?

I am building a neural network for which I am using the sigmoid function as the activation function for the single output neuron at the end. Since the sigmoid function is known to take any number and ...
287 views

### Why do non-linear activation functions that produce values larger than 1 or smaller than 0 work?

Why do non-linear activation functions that produce values larger than 1 or smaller than 0 work? My understanding is that neurons can only produce values between 0 and 1, and that this assumption can ...