Can a micron sized sack of interacting molecules autonomously learn an internal
model of a complex and fluctuating environment? We draw insights from control
theory, machine learning theory, chemical reaction network theory, and statistical
physics to develop a general architecture whereby a broad class of chemical systems
can autonomously learn complex distributions. Our construction takes the form of
a chemical implementation of machine learning’s optimization workhorse: gradient
descent on the relative entropy cost function which we demonstrate can be viewed
as a form of integral feedback control. We show how this method can be applied to
optimize any detailed balanced chemical reaction network and that the construction
is capable of using hidden units to learn complex distributions.