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Can a micron sized sack of interacting molecules autonomously learn aninternal model of a complex and fluctuating environment? We draw insights fromcontrol theory, machine learning theory, chemical reaction network theory, andstatistical physics to develop a general architecture whereby a broad class ofchemical systems can autonomously learn complex distributions. Our constructiontakes the form of a chemical implementation of machine learning's optimizationworkhorse: gradient descent on the relative entropy cost function. We show howthis method can be applied to optimize any detailed balanced chemical reactionnetwork and that the construction is capable of using hidden units to learncomplex distributions. This result is then recast as a form of integralfeedback control. Finally, due to our use of an explicit physical model oflearning, we are able to derive thermodynamic costs and trade-offs associatedto this process.

Autonomous Learning of Generative Models with Chemical Reaction Network Ensembles