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 ...
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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 ...
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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 ...
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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 ...
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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-...
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ignoring instances or masking by zero in multitask learning model

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 ...
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In logistic regression, why is the binary cross-entropy loss function convex?

I am studying logistic regression for binary classification. The loss function used is cross-entropy. For a given input $x$, if our model outputs $\hat{y}$ instead of $y$, the loss is given by $$\text{...
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How do I implement the cross-entropy-method for a RL environment with a continuous action space?

I found many tutorials and posts on how to solve RL environments with discrete action spaces using the cross entropy method (e.g., in this blog post for the OpenAI Gym frozen lake environment). ...
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What error should I use for RNN?

I'm relatively new to machine learning, and I don't know what error I should use for an RNN. I want to use a simple Elman RNN to predict the cases of Covid-19 there will be in a hospital for the next ...
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How to compute the gradient of the cross-entropy loss function with respect to the parameters with softmax activation function?

I've seen plenty of examples of people doing Sigmoid + MSE backpropagation implementations, yet I do not seem to understand how to implement backpropagation as stated in the title in the case of multi-...
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Have I understood the loss function from the original U-Net paper correctly?

In the original U-Net paper, it is written The energy function is computed by a pixel-wise soft-max over the final feature map combined with the cross entropy loss function. ... $$ E=\sum_{\mathbf{x} ...
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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)] \...
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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 ...
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Why are there two versions of softmax cross entropy? Which one to use in what situation?

I have seen 2 forms of softmax cross-entropy loss and are confused by the two. Which one is the right one? For example in this Quora answer, there are 2 answers: $L(\mathbf{w})=\frac{1}{N} \sum_{n=1}^...
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What is the advantage of using cross entropy loss & softmax?

I am trying to do the standard MNIST dataset image recognition test with a standard feed forward NN, but my network failed pretty badly. Now I have debugged it quite a lot and found & fixed some ...
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Loss function for better class separability in multi class classification

So I am trying to enforce better separability in my deep learning model and was wondering what I can use besides cross entropy loss to do that? Could maybe using logarithm with different basis in ...
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Which loss function should I use in REINFORCE, and what are the labels?

I understand that this is the update for the parameters of a policy in REINFORCE: $$ \Delta \theta_{t}=\alpha \nabla_{\theta} \log \pi_{\theta}\left(a_{t} \mid s_{t}\right) v_{t}, $$ where $v_t$ is ...
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How do you manage negative rewards in policy gradients?

This old question has no definitive answer yet, that's why I am asking it here again. I also asked this same question here. If I'm doing policy gradient in Keras, using a loss of the form: ...
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How are weights for weighted x-entropy loss on imbalanced data calculated?

I am trying to build a classifier which should be trained with the cross entropy loss. The training data is highly class-imbalanced. To tackle this, I've gone through the advice of the tensorflow docs ...
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Is maximum likelihood estimation meaningless for a dataset of only outliers?

From my understanding, maximum likelihood estimation chooses the set of parameters for the estimator that maximizes likelihood with the ground truth distribution. I always interpreted it as the ...
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Can the cross-entropy loss be used for a NLP task with LSTM?

I am trying to build an LSTM model to generate Shakspeare-like poems. I have training set $\{s_1,s_2, \dots,s_m\}$, which are sentences of Shakespeare poems, and each sentence contains words $\{w_1,...
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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, ...
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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 ...
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1 answer
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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 ...
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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 ...
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4 votes
1 answer
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 ...
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7 votes
1 answer
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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 ...
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2 votes
2 answers
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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 ...
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18 votes
1 answer
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Why has the cross-entropy become the classification standard loss function and not Kullback-Leibler divergence?

The cross-entropy is identical to the KL divergence plus the entropy of the target distribution. The KL divergence equals zero when the two distributions are the same, which seems more intuitive to me ...
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9 votes
2 answers
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How do I handle negative rewards in policy gradients with the cross-entropy loss function?

I am using policy gradients in my reinforcement learning algorithm, and occasionally my environment provides a severe penalty (i.e. negative reward) when a wrong move is made. I'm using a neural ...
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