Maybe it isn&#x27;t, but I have found the literature on the topic to be very clear in general. I do not find section 1.5 and 2.3 explicit at all.<p>Section 2.3 reads like a redefinition of the exponential family and its link to the maximum entropy principle. I think the idea is to optimize the sufficient statistics, but it&#x27;s not clear.<p>Section 1.5... well you talk about two dimensional translational symmetries, and then make a link with position and momentum, but where is that coming from? This seems merely like an artifact of looking at two dimensional translational symmetries, and not at the general case. Again, what does the quantum analogy bring to the table? I think - though it&#x27;s not clear - that what you&#x27;re suggesting is drawing the latent noise following a distribution which is reflects the expected symmetry in the manifold.<p>So what is the takeout? Are you attempting to parametrize max-entropy distribution using the symmetries as constraints?