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.

翻译：一个微米大小的分子相互作用囊能否自主学习复杂波动环境的内部模型？我们从控制理论、机器学习理论、化学反应网络理论和统计物理学中汲取洞见，开发了一种通用架构，使广泛类别的化学系统能够自主学习复杂分布。我们的构建形式采用了机器学习优化工具的化学实现：在相对熵代价函数上进行梯度下降。我们展示了该方法如何应用于优化任意细致平衡的化学反应网络，并证明该构建能够利用隐藏单元学习复杂分布。随后，这一结果被重新诠释为一种积分反馈控制形式。最后，由于我们采用了显式的学习物理模型，因此能够推导出与此过程相关的热力学代价与权衡。