Not really. The sentence with the King was used to mean that the new King immediately got into function.

> Le Roi (Louis ##) est mort. Vive le Roi (Louis ## + 1) !

Using the sentence with Deep Learning and Differential Learning just suggests that Differential Learning is the heir/successor/evolution of Deep Learning. It does not imply that they are the same thing.

As a French person used to the saying, Le Cun probably meant that.

It does, actually. What matters is that there is a king, not who is the king.

The saying works because, as you say, it suggests a successor, but the successor has to use the same title, because what people want is a new king, so that nothing changes and they can live as they did before the king was dead, not a revolution with a civil war tainted in blood.

If you do volontarily change the title, it's because you think the new one will be better, which is pretentious.

> Using the sentence with Deep Learning and Differential Learning just shows how Differential Learning is an evolution. It does not imply that they are the same thing.

... where did I imply it means they're the same thing?

From my comment:

> indicate it’s not a totally new thing but a significant shift in how it’s done

You could say, an evolution?

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A snowclone is a statement in a certain form. The relevant form that English speakers use (I'm not a French person, and this is an English article) is "X is dead, long live X", where both are X.

That's where the "joking" the above comment is referring to comes from, it sounds "nonsensical" if you take it literally.

If you change one X to Y, suddenly there's no tongue-in-cheek aspect, you're just saying "that thing sucks, this is the new hotness".

I suspect the author just missed that nuance or got caught up in their excitement, but the whole point of a snowclone is it has a formula, and by customizing the variable parts of that formula, you add a new subtle meaning or tint to the statement.