# Tag Info

## Hot answers tagged objective-functions

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### Loss jumps abruptly when I decay the learning rate with Adam optimizer in PyTorch

I see no reason why decaying learning rates should create the kinds of jumps in losses that you are observing. It should "slow down" how quickly you "move", which in the case of a loss that otherwise ...
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### What loss function to use when labels are probabilities?

Actually, the cross-entropy loss function would be appropriate here, since it measures the "distance" between a distribution $q$ and the "true" distribution $p$. You are right, ...
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### Can the mean squared error be negative?

In general a cost function can be negative. The more negative, the better of course, because you are measuring a cost the objective is to minimise it. A standard Mean Squared Error function cannot be ...
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### Which function $(\hat{y} - y)^2$ or $(y - \hat{y})^2$ should I use to compute the gradient?

The derivative of $\mathcal{L_1}(y, x) = (\hat{y} - y)^2 = (f(x) - y)^2$ with respect to $\hat{y}$, where $f$ is the model and $\hat{y} = f(x)$ is the output of the model, is \begin{align} \frac{d}{...
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### Which function $(\hat{y} - y)^2$ or $(y - \hat{y})^2$ should I use to compute the gradient?

The MSE can be defined as $(\hat{y} - y)^2$, which should be equivalent to $(y - \hat{y})^2$ They are not just "equivalent". It is actually the exact same function, with two different ways to write ...
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### What is the formula used to calculate the loss in the FaceNet model?

The loss function used is the triplet loss function. Let me explain it part by part. Notation The $f^a_i$ means the anchor input image. The $f^p_i$ means the <...
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### In which cases is the categorical cross-entropy better than the mean squared error?

As a rule of thumb, mean squared error (MSE) is more appropriate for regression problems, that is, problems where the output is a numerical value (i.e. a floating-point number or, in general, a real ...
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