In

reality, when you are developing a neural network for a machine learning problem,

often times you would need to design a learning objective or network architecture that

is customized towards the problem. A typical challenge in these cases is to make the

forward computation differentiable. An example problem of such would be one that

involves first$-$order logic. e$.$g$.$ How can we enforce logical constraints to the output of

your neural network model?

Suppose you are designing a multi$-$label $($i$.$e$.$ The model outputs multiple labels for

a single input example$)$ image classification model for animal taxonomy. Among the

labels, there are $\{$hamster$,$ cat, mammal$\}.$ Ideally, the model should output mammal