"Therefore, cross entropy can be interpreted as the expected message-length per datum when a wrong distribution Q is assumed while the data actually follows a distribution P. That is why the expectation is taken over the probability distribution P and not Q." --https://en.wikipedia.org/wiki/Cross_entropy

Architectures? I don't know what that means in this context.

Distribution means pmf? What is "ground truth"?

Is the prior reassigned the value of the posterior between updates?

=log(Q/P) goes to infinity when P goes to 0, and goes to negative infinity as Q goes to 0.

modes = likelihood maximizers?

Let p(X) denote the prior. Then: posterior = p(X|out) = P(X,out)/P(out) = p(out|X)/p(out) p(X)

cov(x,y)=E[(x-E(x))(y-E(y)]

Schrödinger's cat/dog

And then use Bayesian methods to determine which segmentations are more likely.