Neural CRNs: A Natural Implementation of Learning in Chemical Reaction Networks

Abstract: This work introduces Neural CRNs, a general-purpose chemical neural network framework that embeds learning directly into mass-action chemical reaction systems. Unlike prior approaches that chemically implement and compose discrete neural computations, Neural CRNs adopt an analog computing approach, where both forward and backward passes of learning are implemented as continuous-time evolutions of molecular concentrations. Such an analog formulation naturally aligns with the analog nature of chemical kinetics, yielding concise circuits and practicable reactions. We demonstrate this efficiency by constructing a streamlined supervised learning procedure executable in just two sequential stages. We then implement several learning circuits to demonstrate the framework's linear and nonlinear modeling capabilities and to validate its learning procedure. These circuits are implemented entirely using unimolecular and bimolecular reactions, avoiding the complexity of higher-order chemistries. In summary, Neural CRNs offer a compact, scalable, and autonomous framework for biochemical learning, opening new avenues for adaptive computing in synthetic biology, bioengineering, and biomedicine.