Inspired by natural biochemicals that perform complex information processing within living cells, we design and simulate a chemically implemented feedforward neural network, which learns by a novel chemical-reaction-based analogue of backpropagation. Our network is implemented in a simulated chemical system, where individual neurons are separated from each other by semipermeable cell-like membranes. Our compartmentalized, modular design allows a variety of network topologies to be constructed from the same building blocks. This brings us towards general-purpose, adaptive learning in chemico: wet machine learning in an embodied dynamical system.

Autonomous learning implemented purely by means of a synthetic chemical system has not been previously realized. Learning promotes reusability and minimizes the system design to simple input-output specification. In this article we introduce a chemical perceptron, the first full-featured implementation of a perceptron in an artificial (simulated) chemistry. A perceptron is the simplest system capable of learning, inspired by the functioning of a biological neuron. Our artificial chemistry is deterministic and discrete-time, and follows Michaelis-Menten kinetics. We present two models, the weight-loop perceptron and the weight-race perceptron, which represent two possible strategies for a chemical implementation of linear integration and threshold. Both chemical perceptrons can successfully identify all 14 linearly separable two-input logic functions and maintain high robustness against rate-constant perturbations. We suggest that DNA strand displacement could, in principle, provide an implementation substrate for our model, allowing the chemical perceptron to perform reusable, programmable, and adaptable wet biochemical computing.