  A trivializing map is a field transformation whose Jacobian determinant
exactly cancels the interaction terms in the action, providing a representation
of the theory in terms of a deterministic transformation of a distribution from
which sampling is trivial. Recently, a proof-of-principle study by Albergo,
Kanwar and Shanahan [arXiv:1904.12072] demonstrated that approximations of
trivializing maps can be `machine-learned' by a class of invertible,
differentiable neural models called \textit{normalizing flows}. By ensuring
that the Jacobian determinant can be computed efficiently, asymptotically exact
sampling from the theory of interest can be performed by drawing samples from a
simple distribution and passing them through the network. From a theoretical
perspective, this approach has the potential to become more efficient than
traditional Markov Chain Monte Carlo sampling techniques, where
autocorrelations severely diminish the sampling efficiency as one approaches
the continuum limit. A major caveat is that it is not yet understood how the
size of models and the cost of training them is expected to scale. As a first
step, we have conducted an exploratory scaling study using two-dimensional
$\phi^4$ with up to $20^2$ lattice sites. Although the scope of our study is
limited to a particular model architecture and training algorithm, initial
results paint an interesting picture in which training costs grow very quickly
indeed. We describe a candidate explanation for the poor scaling, and outline
our intentions to clarify the situation in future work.
