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. 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. This result is then recast as a form of integral
feedback control. Finally, due to our use of an explicit physical model of
learning, we are able to derive thermodynamic costs and trade-offs associated
to this process.

微米级袋状互动分子可以自主学习复杂且波动的环境；通过控制理论、机器学习理论、化学反应网络理论和统计物理学，我们开发了一个通用架构，使得广泛类别的化学系统可以自主学习复杂分布。