Automatic Implementation of Neural Networks Through Reaction Networks—Part I: Circuit Design and Convergence Analysis

Rapid advancements of artificial neural networks for computer sciences, inspired by biological neuron interaction mechanisms, may be leveraged in reverse to synthetic biology by providing advanced molecular programming paradigms capable of autonomously learning and executing complex tasks. A challenging exploration is to implement neural network functionalities through biochemical reaction networks (BCRNs), a language that is inherently compatible with in vivo, with difficulties especially in constructing an appropriate BCRN that respects computation and information processing steps involved in neural networks. These two-part articles finish programming a nonlinear fully connected neural network (FCNN) with a three-layer structure using BCRNs endowed with mass action kinetics. In part I, we divide the FCNN into assignment, feedforward propagation, judgment, learning, and clear-out modules. Each module is programmed using BCRNs by setting species concentrations to carry information related to all kinds of computations and operations, with the equilibria of some species to represent the computation results and information processing results. The newly formed biochemical neural network exhibits the potential to work independently in vivo. In addition, our construction addresses a critical design gap by integrating two essential modules: the biochemical assignment module that enables iterative input of training samples, and the biochemical judgment module responsible for determining the termination of the training process. We further confirm theoretically that the BCRN system achieves FCNN functionality with exponential convergence to all target computational results. Finally, the performance of this construction is evaluated numerically on binary classification problems.