  The vast majority of work in self-supervised learning, both theoretical and
empirical (though mostly the latter), have largely focused on recovering good
features for downstream tasks, with the definition of "good" often being
intricately tied to the downstream task itself. This lens is undoubtedly very
interesting, but suffers from the problem that there isn't a "canonical" set of
downstream tasks to focus on -- in practice, this problem is usually resolved
by competing on the benchmark dataset du jour.
  In this paper, we present an alternative lens: one of parameter
identifiability. More precisely, we consider data coming from a parametric
probabilistic model, and train a self-supervised learning predictor with a
suitably chosen parametric form. Then, we ask whether we can read off the
ground truth parameters of the probabilistic model from the optimal predictor.
We focus on the widely used self-supervised learning method of predicting
masked tokens, which is popular for both natural languages and visual data.
  While incarnations of this approach have already been successfully used for
simpler probabilistic models (e.g. learning fully-observed undirected graphical
models), we focus instead on latent-variable models capturing sequential
structures -- namely Hidden Markov Models with both discrete and conditionally
Gaussian observations. We show that there is a rich landscape of possibilities,
out of which some prediction tasks yield identifiability, while others do not.
Our results, borne of a theoretical grounding of self-supervised learning,
could thus potentially beneficially inform practice. Moreover, we uncover close
connections with uniqueness of tensor rank decompositions -- a widely used tool
in studying identifiability through the lens of the method of moments.
