  This paper is concerned with programming adaptive linear neural networks
(ALNNs) using chemical reaction networks (CRNs) equipped with mass-action
kinetics. Through individually programming the forward propagation and the
backpropagation of ALNNs, and also utilizing the permeation walls technique, we
construct a powerful CRN possessing the function of ALNNs, especially having
the function of automatic computation. We also provide theoretical analysis and
a case study to support our construction. The results will have potential
implications for the developments of synthetic biology, molecular computer and
artificial intelligence.
