Notably, when the system undergoes phase change, there’s not just a change in values of the natural latents (like e.g. whether the consensus direction is up or down), but also in what variables are natural latents (i.e. what function to compute from a chunk in order to estimate the natural latent). In our work, we think of this as the defining feature of “phase change”; it’s a useful definition which generalizes intuitively to other domains.
The way the book talks about this, it almost seems like systems on critical points are systems where previous abstractions you can usually use break down. For example, these are associated with non-local interactions, correlations (here used as a sort of similarity/distance metric) which become infinite, and massive restructuring events. Also, in the classical natural abstractions framing, if you freeze water, you go from the water being described by a really complicated energy-minimization-subject-to-constant-volume equation to like 6 parameters.
Which has influenced non-trivially my optimism in singular learning theory, and the devinterp-via-phase-transitions paradigm. Glad to see y’all think about this the same way.
When I was first learning about the Ising model while reading Introduction to the Theory of Complex Systems, I wrote down this note:
Which has influenced non-trivially my optimism in singular learning theory, and the devinterp-via-phase-transitions paradigm. Glad to see y’all think about this the same way.