# Is Categorical Crossentropy Loss always bounded in the [0, 1] interval?

Is Categorical Crossentropy always bounded between 0 and 1, or is it possible that during training of a Neural Network it can get higher values?

More specifically, I'm referring to the TensorFlow 2.0 function.

You can actually get values from $$[0, \infty[$$. Consider the cross entropy loss be following formula:
$$loss (y_{pred}, y_{true}) = - \log{y_{pred, class_i}}$$
, whereas the index $$class_i$$ states that you only use the output of the $$i$$th class.
For example think that your true class is $$dog$$, which is represented by the $$3$$rd output neuron. On the $$3$$rd output neuron your network outputs a probability of $$10\%$$. Your loss is then $$-\log{10\%}= 2.3$$. Further if your probability is only $$0.1\%$$ your loss will equal $$6.9$$ and so on.
$$\lim\limits_{x \rightarrow 0}{\log{x}} = -\infty$$